This article presents a design methodology for non-stationary dissipative controllers applicable to Markov jump systems (MJSs) operating under multiple time-varying delays. A key contribution of this work is the use of distinct mode-dependent (MD) structures for the controlled system and the controller, governed by a stationary Markov chain τ(k) and a non-stationary Markov chain σ(k), respectively. A novel feature of this study is its account for general transition probabilities (GTPs) in two distinct Markov chains, where the probabilities are not fully known, which constitutes a significant extension of existing frameworks. Furthermore, our model of the MJSs fully incorporates multiple mode-dependent (MD) time-varying delays, denoted as d1τ(k)(k), d2τ(k)(k), and d3σ(k)(k). Leveraging Lyapunov stability theory and stochastic analysis, we obtain a sufficient condition that guarantees both the stochastic stability of the resulting closed-loop MJSs and a prescribed (Q,S,R)−γ−dissipative performance level. Finally, the feasibility and validation of the presented control strategy are demonstrated via two numerical examples.
Tracking time-varying references in underactuated systems is a challenging issue in automatic control. This paper presents the design and analysis of an energy shaping control law for a self-balancing robot. The proposed control law guarantees that the discrepancy between the coordinates of the self-balancing robot and a temporal function serving as a reference for the wheels remains contained within bounds, provided that the trajectories themselves are bounded. The theoretical findings are corroborated by real-time experimental results that illustrate the efficacy of the proposed control law with different initial condition and in the presence of disturbances. To the authors’ knowledge, this represents the first control strategy utilizing energy shaping that is capable of executing the specified task in a system with a non constant inertia matrix dependent on the non actuated joint along with potential energy.
This paper investigates the rendezvous problems of leader-following and leaderless consensus for multiple unmanned aerial vehicle (UAV) systems under a sampled-data approach. In contrast to existing sampled-data fault-tolerant control approaches that typically address actuator faults, sensor faults, or packet losses separately, the proposed method handles combined actuator and sensor faults together with random packet losses in the communication network. An H∞ sampled-data-based FTC scheme is systematically developed to enhance robustness against disturbances and network-induced uncertainties. By constructing a refined Lyapunov–Krasovskii functional and employing Wirtinger-based integral inequalities along with Kronecker product theory, less conservative stability conditions are derived. Furthermore, an explicit relationship between sampling intervals and network-induced delays is established, providing improved feasibility compared to closely related sampled-data consensus results. The proposed approach guarantees both leader-following and leaderless rendezvous while effectively compensating for multiple fault types and stochastic packet losses within a unified approach. The effectiveness and reduced conservatism of the developed method are demonstrated through three comprehensive numerical examples.
This paper presents a comprehensive framework for robust control and active fault-tolerant operation of overhead crane systems transporting liquid payloads under nonlinear dynamics, external disturbances, and actuator faults. A novel dynamic modeling approach is developed that explicitly incorporates the coupled hook-container dynamics and nonlinear liquid sloshing effects, providing a realistic representation of the flexible coupling and energy exchange mechanisms inherent in practical crane operations. To address the challenges of vibration suppression and precise positioning under harsh operating conditions, a Multi-Objective Constrained Linear Matrix Inequality-Integrated Sliding Surface Controller (MO-Constrained LMI-ISSC) is proposed. The controller systematically integrates H∞ disturbance attenuation, decay rate constraints for transient regulation, and explicit input-output constraints within a unified sliding mode control framework, ensuring robust performance while satisfying physical and safety requirements. Furthermore, an active fault-tolerant control scheme is established by integrating a Full-Order Fault Estimation Observer (FFEO) designed using frequency-domain-dependent H∞ performance criteria based on the generalized Kalman-Yakubovich-Popov (KYP) lemma. This observer-based approach enables simultaneous actuator fault reconstruction and disturbance attenuation with reduced conservatism compared to conventional full-band designs. The estimated fault information is utilized for online compensation, enhancing system reliability and operational safety under faulty conditions. Simulation results demonstrate the effectiveness of the proposed integrated framework in achieving improved precise positioning, vibration suppression, and fault tolerance in safety-critical liquid transportation applications.
This paper discusses the distributed fusion filtering (DFF) problem for a type of discrete-time nonlinear systems subject to missing measurements with uncertain probabilities and accumulation-based event-triggered scheme (ETS). The missing measurements are taken into account in system and missing probabilities are considered with uncertain probabilities, better reflecting the reality scene. In addition, the accumulation-based ETS is introduced to enhance system performance while maintaining robustness against signal fluctuations. For the addressed DFF issue, the main goal of this paper is to derive a fusion filter in accordance with the inverse covariance intersection fusion rule. Specifically, the local filter is designed and filtering error (FE) covariance derived. Furthermore, the upper bound of the local FE covariance can be obtained and minimized by selecting the appropriate filter gain. In addition, the boundedness of the filtering performance is analyzed. Finally, two numerical examples are used to demonstrate the usefulness of the proposed DFF approach.
The marine environment is subjected to several uncertainties, such as underwater currents, water pressure, and several other factors. This leads to an irregular maritime environment, which renders it hard for autonomous underwater vehicles (AUVs) to maneuver, relate to their environments, and endure for a longer duration. Besides, the buoyancy, mass error, or hydrodynamic coefficients of the vehicle can further complicate its motion. When operated in real-time, the aforesaid issues challenge the control community to design effective, robust control strategies ensuring stability. This work explains the design of a robust stabilization approach by exploring the AUV system. The concept of reverse input constraints is applied to explain the robust control design, which is illustrated in the diving plane. The robust stabilization approach is considered by incorporating the uncertainties into the AUV system. In addition, the stability of the system is explained through the Lyapunov function. Despite uncertainties in the AUV system, the desired depth is achieved. Furthermore, a comparison is made with the adaptive fuzzy sliding mode control (AFSMC) to ensure the acceptability of the proposed control approach (improvement of 4.9% and 3.8% in settling time relating to the actuator and sensor fault, respectively).
This paper focuses on designing robust event-triggered sampled-data controllers for uncertain linear systems. The proposed controllers aim to ensure robust stability and guaranteed performance while adhering to minimum dwell-time constraints. To achieve this, we introduce a hybrid system model to represent the closed-loop dynamics, which is then used to derive sufficient design conditions based on differential matrix inequalities, which are convex for a fixed parameter. Numerical examples are included to demonstrate the key features and effectiveness of the proposed approach.
In this paper, the problem of the motion coordination control of a moving ground robot and a quadrotor unmanned aerial vehicle with limited field-of-view (FOV) and limited communication range is addressed. By using the prescribed performance technique, a new controller is proposed to maintain a quadrotor over the moving ground robot such that the robot continuously lies inside the camera FOV, the communication link between both vehicles is preserved and no collision occurs between them. Undesirable deviations between both vehicles are effectively avoided during the turning of the ground robot by compensating for the path curvature. By employing the command-filtered backstepping control method, the first and second-order derivative terms of reference command signals are reconstructed. By an efficient combination of a radial basis function neural network (RBFNN) and an adaptive robust controller, model uncertainties, wind disturbances and neural network approximation errors are well compensated. To evaluate the performance of the proposed controller, computer simulations have been done in MATLAB software and according to the obtained results, it will be shown that the tracking errors between the quadrotor and moving robot at a certain distance have been converged to zero within a small time while a circular trajectory has been tracked despite the applied wind disturbances.
This article proposes a hybrid extended state observer (HyESO)-based prescribed performance full-state constrained control scheme for electrohydraulic servo systems under the coexistence of matched and mismatched disturbances. The designed HyESO simultaneously estimates and compensates for these two disturbance types, thereby enhancing disturbance rejection capability. Full-state constraints are explicitly enforced via a barrier Lyapunov function (BLF), while a prescribed performance function (PPF) is introduced to shape both transient and steady-state behaviors of the compensated tracking error within predefined bounds. To reduce the complexity of traditional backstepping design and avoid the “explosion of complexity” issue, a command-filtering technique is introduced. And an error-compensation mechanism is incorporated to reduce the adverse influence of filtering errors. Then rigorous analysis guarantees that the tracking error converges to a small neighborhood of zero and all closed-loop signals are bounded, while the prescribed performance requirements are satisfied. Finally, four simulation cases are carried out for comparative purposes to demonstrate the effectiveness, robustness, and superiority of the proposed method.
Ensuring accurate tracking for wheeled mobile robots (WMRs) while avoiding obstacles in complex environments is a crucial challenge. Existing methods often involve complex structures, suffer from high computational demands, or lack a unified mechanism to simultaneously ensure robust tracking, obstacle avoidance (OA), and safety under disturbances. Therefore, there is a need for a simple real-time control architecture that reduces computational burden while ensuring safe OA and robust trajectory tracking (TT). In response to this challenge, this paper proposes a novel robust safety tracking control approach to address the dual objectives of OA and TT under disturbances with two-fold ideas: 1) a robust nonsingular fast terminal sliding mode control (RNFTSMC) tracking algorithm integrated with an extended state observer (ESO), where the underactuated WMR model is first transformed into a linear canonical form using differential flatness, thereby facilitating the design of a stabilizing feedback controller to compensate for uncertainties and disturbances, ensure precise TT, minimize chattering, mitigate perturbations, avoid singularity issues, and achieve rapid convergence, and 2) a control barrier function (CBF)-based quadratic programming (QP) safety mechanism. The feedback controller is combined with safety constraints embedded in a QP formulation to ensure safe navigation in obstacle-rich environments and enable simultaneous robust TT and OA. The theoretical contribution lies in the formulation of robust tracking and safety controllers, along with stability and safety analysis proving finite-time convergence of tracking errors and forward invariance of the safe set under bounded disturbances. Finally, simulation and experimental results validate the proposed method’s effectiveness.
For many control systems, the presence of perturbations decreases performance, hence their rejection has been an active area of research for decades. Roughly speaking, there are two kinds of perturbations, those which are matched, i.e. the control input can act directly on them, and those which are mismatched. This paper combines and improves previous results by the authors using a fixed-time singularity-free Sliding Mode Control (SMC) approach to fully reject matched disturbances for a class of nonlinear systems, while it is shown that mismatched perturbations can be attenuated up to an arbitrarily small ultimate bound which depends only on design parameters. Together with two other examples, it is shown how the general scheme can be applied to unicycle-type mobile robots, well-known for being a challenging class of nonholonomic systems. Simulation results are provided to validate the proposed theory.
This work presents a novel Anticipatory Reflexive Control with Stochastic Memory Encoding (ARC-SME) which incorporates Curvature-Aware Goal-Tracking Control with Adaptive Energy Shaping (CAGE) controller for real-time navigation of Unmanned Aerial Vehicles (UAVs) in environments populated with moving obstacles exhibiting uncertain and nondeterministic behavior. The proposed control architecture integrates a biologically inspired dual-layer structure comprising: (i) a reflexive feedback controller that provides high-frequency reactive avoidance based on instantaneous obstacle proximity gradients, and (ii) an anticipatory feedforward controller that leverages future state predictions of dynamic obstacles through a stochastic motion model. Central to this architecture is the Stochastic Memory Encoding (SME) layer, which encodes historical spatiotemporal obstacle risk distributions using a fading-memory model. This encoding dynamically modulates the relative contributions of the reflexive and anticipatory controllers. In tandem with CAGE, Predictive and Adaptive Risk-Aware Spatio-Temporal Rapidly-Exploring Random Tree (RRT) (PRAST-RRT) has been proposed for high-level global path planning. The Encoder-Decoder LSTM architecture has been included to forecast the future trajectories of moving obstacles based on their previous motion. Hardware-in-the-Loop (HIL) with Simulink and MATLAB Function Blocks has been used to test the efficacy of the proposed work. Simulation results in sparse dynamic environments, dense dynamic environments, mixed static dynamic clutter, and adversarial scenarios demonstrate that ARC-SME with CAGE achieves superior performance in terms of collision avoidance rate, energy efficiency, and path smoothness compared to conventional techniques.
Coprime factorizations are important for the characterization and construction of stabilizing controllers. Formulae for both right- and left-coprime factorizations of well-posed infinite-dimensional systems exist in terms of the state-space formulation. Many such systems arise as boundary control systems, and constructing the state-space formulation is an additional step that may be cumbersome. This work presents formulae for the coprime factorization and the corresponding Bézout factors of well-posed boundary-controlled systems as boundary control systems. Several examples are provided to illustrate construction of the coprime factors.
This paper investigates safe and high-performance liquid transportation using a Biglide parallel robot. Although the Biglide mechanism enables fast planar motion, transporting a liquid-filled container induces sloshing due to the coupling between robot motion and the liquid free surface. The main challenge is to simultaneously achieve accurate trajectory tracking and suppress liquid sloshing during high-speed motion. To reduce sloshing excitation from the planning stage, a smooth S-curve trajectory is designed, and Ant Colony Optimization (ACO) is employed to obtain time-optimal trajectory parameters. For closed-loop control, a PPC-HTSMC-ESO framework is proposed. In this framework, Hierarchical Terminal Sliding Mode Control (HTSMC) provides finite-time robust tracking of the optimized trajectory, Prescribed Performance Control (PPC) constraints the sloshing-related error within a prescribed performance envelope, and Extended State Observer (ESO) estimates unmeasured states and lumped disturbances for real-time compensation. The main contribution is the combination of a time-optimal S-curve trajectory and a PPC-HTSMC-ESO controller. The trajectory reduces sloshing excitation before motion execution, while the controller ensures accurate tracking, bounded sloshing response, and disturbance rejection during transportation. Simulation results demonstrate that the integrated method achieves accurate trajectory tracking, strong robustness, and significant sloshing suppression, confirming its suitability for liquid-transport tasks in industrial applications.
Following the recent approach of the authors Nicolau et al. (2024), this paper further analyzes relationships between mechanical flatness, the underlying mechanical structure of the system, and different variants of differential flatness, in particular, configurational flatness. For the class of mechanical control systems with n degrees of freedom and n−1 inputs, we establish a general classification result in terms of normal forms, emphasizing the connections between mechanical flatness, configuration flatness, and static mechanical feedback linearization. Moreover, in the case where the distribution, spanned on the configuration manifold by control vector fields, is involutive, we provide geometric verifiable characterizations of both config-flatness and mechanical flatness.
This paper introduces a novel approach to control a boundary-actuated semilinear parabolic system. To convey the core aspects of the design, an exemplary diffusion-reaction PDE is considered for simplicity. After a flatness-based state transformation into an infinite-dimensional system of ODEs in strict-feedback form, classical integrator backstepping is applied recursively. This enables the design of an exactly-linearizing state feedback of so-called flat coordinates, mapping the system into a linear target system with desired stability reserve. Based on the linear equations of the target system in closed loop, a controller is designed for trajectory tracking in the transformed coordinates. The flatness-based transformation and the resulting control law are traced back to the solution of an appropriate linear Cauchy problem that depends on the system state. An efficient numerical scheme is proposed to approximate the solution of the Cauchy problem and, thus, obtain an online approximation of the control law. Simulation results demonstrate the practicability of the design and illustrate the control performance.
A fundamental issue in control applications is ensuring performance and stability in the presence of modeling uncertainties and external disturbances. In this regard, in recent years the integration of Sliding Mode Control (SMC) with Model Predictive Control (MPC) has proven particularly effective, combining the intrinsic robustness of SMC with MPC’s ability to handle constraints and provide optimal performance. In this context, Integral Sliding Mode Predictive Control (ISMPC) has emerged as a promising approach. Despite this practical relevance, relatively few studies in the literature address discrete-time, observer-based implementations of ISMPC when the full state is not available and noisy output measurements must be used. In particular, the application of ISMPC to collocated electromechanical systems presents the issue of dealing with invariant zeros. In this work, three discrete-time observer implementations, namely, a standard Discrete-time Sliding Mode Observer (DSMO), a DSMO variant named the Direct Output Injection Estimator (DOIE), and an Unknown Input Observer (UIO), are analyzed and compared, when used in combination with ISMPC to control a simple two-mass system with friction. Under noisy measurement conditions, both the UIO and DOIE significantly outperform the DSMO; while the UIO provides the highest theoretical robustness, the DOIE delivers comparable performance with minimal tuning effort.
The H∞ norm is a widely used metric to assess the performance of Linear Time-Invariant (LTI) systems. In the presence of uncertainties, guaranteed bounds on the worst-case H∞ norm can be efficiently computed by means of μ-based techniques. However, it is more difficult to obtain a guaranteed lower bound on all possible realizations of an uncertain linear system, particularly in the MIMO case. The precise characterization of such a bound is nevertheless very useful for quickly identifying the uncertainty combinations where an H∞ criterion is not satisfied, and then for deducing reliable bounds on the failure probability of a control law. A new sufficient condition is proposed in this paper for calculating this lower bound. Unlike previous results, our approach does not require any inversion of the system, which therefore does not need to be invertible or even square. The central result of this paper is based on an original use of Weyl’s inequalities, which allow to bound more precisely the maximum singular value (rather than the entire set of singular values) of the uncertain transfer matrix. This new result is then integrated into a Branch-and-Bound (B&B) scheme to improve the calculation of guaranteed bounds on the probability that a given H∞ performance requirement is verified or not. Since it quantifies the probability of rare events, such a probabilistic analysis offers a significant advantage over deterministic worst-case approaches by avoiding the invalidation of a controller on the basis of unlikely failures.
We consider the problem of worst-case Conditional Value at Risk (CVaR) for quadratic loss functions with ambiguity sets determined by the first and the second moments of random vectors. Despite its popularity in recent times, analytical solutions to the worst-case CVaR problem are known only in a very restricted subclass of the problem, making it difficult to solve problems involving worst-case CVaR beyond its computation. In this article, we extend the subclass of worst-case CVaR problems that admits analytical solutions. For a quadratic loss with a semidefinite quadratic term, we reduce the problem to the maximization of a quadratic polynomial over the unit ball with respect to Euclidean norm. Using the same reduction, we derive analytical solutions when the quadratic term is determined by a scaling of the identity matrix. We also derive analytical solutions when the quadratic loss function does not have a linear term. By utilizing those solutions, we also explore the problem of finite-horizon worst-case CVaR optimal control with quadratic loss functions. Restricting to the case of controllers that are linear in past disturbances, we formulate the problem of computing the optimal linear controller as a semidefinite program. Finally, we show that affine controllers are suboptimal by considering scalar dynamics.
