We consider the problem of verifying discretetime dynamical systems against properties specified as universal timed co-Buchi automata. Universal co-Buchi automata capture many important properties such as safety, liveness, and those specified in Linear Temporal Logic. However, such automata do not consider timing constraints. We thus consider the problem of verification against timed automata which combine such properties with timing constraints. Our verification approach relies on first constructing a product of the system, the states of the timed automata, and the valuations of the clocks of the automata. To show that the traces of the system are accepted by the automata, we seek to ensure that they correspond to runs that visit a set of co-B uchi states only finitely often. To prove this, we append a counter value to the product that keeps track of the number of visitations to relevant co-Buchi states. We then search for a so-called timed co-Buchi barrier certificate (TCBC) to show that these states are visited only finitely often. We present a satisfiability modulo theory (SMT)-based approach to find these certificates. Finally, we demonstrate our approach on some case studies.

In this work, we develop a scheme for constructing continuous approximations (referred to as abstractions) of a class of discrete-time control systems with partially unknown dynamics. The abstraction, itself a nonlinear discrete-time control system (preferably with a significantly lower dimension than the original one) can be used as a substitute in the controller design process. The technique consists of using data sampled from the concrete system to find a lower dimensional subspace of its state space (which we call the active subspace), and constructing an abstraction candidate using Gaussian Process (GP) regression. We derive sufficient conditions under which the GP candidate is shown to be the abstraction of the original system while quantifying the error bound between the output of the abstraction and that of the concrete system. A numerical example is presented to illustrate the effectiveness of this approach.

In electromechanical systems, backlash in gear trains can lead to a degradation in control performance. We propose a drive–anti-drive mechanism to address this issue. It consists of two DC motors that operate in opposite directions. One motor acts as the drive, while the other serves as the anti-drive to compensate for the backlash. This work focuses on switching between the drive and anti-drive motors, controlled by a switched-mode PID controller. Simulation results on an inverted pendulum demonstrate that the proposed scheme effectively compensates for backlash, improving position accuracy and control. This switched controller approach enhances the performance of electromechanical systems, particularly where gear backlash poses challenges to closed-loop performance.

In this letter, we propose a data-driven approach for synthesizing safety controllers for unknown nonlinear control systems using Gaussian Process (GP) transfer learning. Our approach involves two steps. The first step involves learning a GP model using data sampled from the system. Our method allows for leveraging a previously learned GP model of a related system, known as the source system (e.g., robot deployed in slightly different environmental conditions), to learn a GP model for the system at hand, known as the target system. This is required in situations where data collection for the target system is expensive or time consuming. In the second step, we compute a control barrier function together with a corresponding controller based on the learned GP model. In addition, we quantify the lower bound on the probability of safety satisfaction for the target system equipped with the synthesized controller. We demonstrate the effectiveness of the proposed approach by applying it to a jet engine case study.

Formal synthesis of controllers for stochastic control systems with unknown models is a challenging problem. In this paper, we focus on safety controller synthesis for nonlinear stochastic control systems. The approach consists of a learning step followed by a controller synthesis scheme using control barrier functions. In the learning phase, we employ Gaussian processes (GP) to learn models of unknown stochastic control systems in the presence of both process and measurement noises. In the controller synthesis phase, we compute control barrier functions together with their corresponding controllers based on the learned GP and quantify lower bounds on the probabilities of safety satisfaction for the original unknown systems equipped with the synthesized controllers. Finally, the effectiveness of the proposed approach is illustrated on a room temperature control and a vehicle lane-keeping example.

In this paper, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a stochastic hybrid system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a class of stochastic hybrid systems involving nonlinearities satisfying an incremental quadratic inequality. In this paper, unlike existing results, the stochastic noises and jumps in the concrete subsystem and its abstraction need not be the same. We provide examples with numerical simulations to illustrate the effectiveness of the proposed dissipativity-type compositional reasoning for interconnected stochastic hybrid systems.

We consider the problem of designing an Image-Based Control (IBC) application mapped to a multiprocessor platform. Sensing in IBC consists of compute-intensive image processing algorithms whose execution times are dependent on image workload. The challenge is that the IBC systems have a high (worst-case) workload with significant workload variations. Designing controllers for such IBC systems typically consider the worst-case workload that results in a long sensing delay with suboptimal quality-of-control (QoC). The challenge is: how to improve the QoC of IBC for a given multiprocessor platform allocation? We present a controller synthesis method based on a Markovian jump linear system (MJLS) formulation considering workload variations. Our method assumes that system knowledge is available for modelling the workload variations as a Markov chain. We compare the MJLS-based method with two relevant control paradigms - LQR control considering worst-case workload, and switched linear control - with respect to QoC and available system knowledge. Our results show that taking into account workload variations in controller design benefits QoC. We then provide design guidelines on the control paradigm to choose for an IBC application given the requirements and the system knowledge.

In this work, we derive sufficient conditions under which compositional abstractions of interconnected systems evolving on Riemannian manifolds can be constructed using the interconnection topology and joint differential dissipativity-type properties of subsystems and their abstractions. This allows for a much broader variety of systems than the ones considered in the existing works defined over Euclidean spaces. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. We provide an example to illustrate the effectiveness of the proposed differential dissipativity-type compositional reasoning for interconnected control systems.

In this work, we derive conditions under which abstractions of networks of stochastic hybrid systems can be constructed compositionally. Proposed conditions leverage the interconnection topology, switching randomly between P different interconnection topologies, and the joint dissipativity-type properties of subsystems and their abstractions. The random switching of the interconnection is modelled by a Markov chain. In the proposed framework, the abstraction, itself a stochastic hybrid system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Finally, we provide an example illustrating the effectiveness of the proposed results by designing a controller enforcing some logic properties over the interconnected abstraction and then refining it to the original interconnected system.

In this work, we derive conditions under which compositional abstractions of networks of control systems, interconnected via some dynamic interconnection topology, can be constructed using the dynamic interconnection and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a class of control systems involving nonlineari-ties satisfying an incremental quadratic inequality. We provide an example to illustrate the effectiveness of the proposed dissipativity-type compositional reasoning by reducing a 150-dimensional nonlinear system to a 3-dimensional one.

In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a stochastic hybrid system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a specific class of stochastic hybrid systems by using the sector property of the system nonlinearity. We provide an example with numerical simulations to illustrate the effectiveness of the proposed dissipativity-type compositional reasoning for interconnected stochastic hybrid systems.

Due to the day by day emergence of automobile industry, improvement in sensor technologies and the need to reduce the occurrence of accident vehicle handling and stability improvement technologies emanating. In this paper a novel H infinity controller via scenario optimization (H-infinity VSO) is presented for Active front steer (AFS) control the aim is to handle and stabilize vehicle under the uncertainty of parameter road adhesion coefficient µ. Parameter uncertainty is translated into perturbed matrixes. Optimal controller gains are calculated by considering predefined scenarios extracted according to the parameters ε and β. ε represents the probability of violation of LMI constraints and β represents confidence or risk failure. In this manner a chance constrained problem is solved which results in less conservativeness in stability and optimality. The results of proposed approach are much improved as compared to the optimal guaranteed cost controller (OGCC) and optimal coordination (OC) controller.

A ball-bot is an extremely agile mobile robotic platform due to its inherent instability. In order to maneuver at high speeds, a specialized controller is needed. A ball-bot can be modelled as two decoupled, 2-DOF pendulum on a cart systems. These systems comprise a classical and frequently encountered problem in the area of control theory. This paper proposed a novel technique for adaptive control of a ball-bot based on inverted pendulum on a cart system using particle swarm optimization (PSO) trained neural network. The generic PID controller is used to control the above mentioned system. The controller is able to learn the demonstrative behavior and keep the pendulum up right when subjected to perturbations. Mean Square Error for training data is found to be 7.68×10−3 and 5.5×10−4 for the testing data. The results show a promising future of the proposed technique.

In the modern era of automotive industry, Active Front Steering (AFS) control is in hot pursuit due to its increased inbuilt vehicle maneuverability, reduced risk of instability and thereby significant reduction in number of accident occurrences. In this paper, a novel control strategy of Model Predictive Controller (MPC) with robust Optimal Guaranteed Cost Controller (OGCC) is introduced for AFS control. In the proposed scheme, MPC is designed to compensate for the effect of the driver's steering input, modeled as a known disturbance. Thus, providing the optimal solution by satisfying control input constraint. The OGCC controller renders the system robustness to the effect of system uncertainties, while achieving acceptable performance for tracking the desired vehicle trajectory. The complete controller scheme achieves the best results with RMS error <; 10-4 and thus whilst guaranteeing the stability of vehicle in the presence of uncertain environment. Numerical simulation results are performed to the effectiveness of the proposed approach over other conventional techniques.

The advent of emerging fields such as networked control systems and wireless sensor networks involving information flow over bandwidth-constrained digital channels has presented the control and information theory communities with a new set of challenges. One of these challenges is to accurately estimate the trajectory of (stochastic) nonlinear systems using sampled and quantized state measurements transmitted over a finite-bandwidth digital channel. This has led researchers to study these problems by combining notions from both control and communication domains, two fields which have been traditionally treated separately. A recent notion introduced in this context is called estimation entropy, which has been defined as the minimum bit rate required to estimate the trajectory of a deterministic nonlinear system with a given exponential convergence rate. In this paper, we show that this notion can be extended to continuous-time stochastic systems as well, particularly, a class of stochastic hybrid systems. We also provide an upper bound on the estimation entropy for this class of systems.

A This paper presents a position tracking control system for a shape memory alloy (SMA) actuator using neural network (NN) feedforward and robust integral of signum of error (RISE) feedback. Nonlinear control of SMA actuators is difficult due to model uncertainties and unknown disturbances. Discontinuous control techniques such as sliding mode control have conventionally been used to achieve asymptotic tracking in the presence of model uncertainties. However, such discontinuous controllers usually result in increased power loss due to high frequency switching. With the recent development of the continuous RISE feedback control, semi-global asymptotic tracking can be achieved. Furthermore, the NN-RISE control leads to better tracking performance and lower power losses caused by input signal switching/chattering when compared to discontinuous controllers. In order to apply the NN-RISE, a state-space model of the SMA actuator is derived, which has been overlooked in many previous works, using Taylor series expansion and exploiting the nature of SMA dynamics. Experimental results show that the proposed control system works well even in the absence of an accurate model of the SMA actuator.

In this paper, we consider improving vehicle handling and stability of road vehicles under model uncertainties using a probabilistic robustness approach. Model based approaches have been extensively explored to tackle the handling and stability problem. However it is known that the performance under such techniques can degrade if uncertainties in model are not taken into account. Many severe accidents result from loss of stability directly or indirectly, which may be attributed to emergency steering, tire pressure loss and different road surface adhesion in the vehicle model. One approach to cater for uncertainties is optimal guaranteed cost controller (OGCC), X. Yang, Z. Wang, and W. Peng [2008], which follows the worst case methodology of robust control design. In this paper, we aim to enhance the performance of the system by formulating the uncertainties as a stochastic phenomenon endowed with a probability measure. Inspired by recent major result in probabilistic convex optimization, we guarantee a priori probabilistic robustness while allowing for certain violation of the underlying constraints of the optimization problem. Numerical simulation results show a marked improvement in results in comparison to the optimal cost (OC) and OGCC approaches.

In this work, we present the application of a neural network (NN) based adaptive control scheme for the purpose of trajectory tracking of an air-to-air missile. The nonlinear dynamic model of such missiles contain numerous aerodynamic coefficients. It is well known that uncertainty in these coefficients can cause degradation of control performance. In this work, we explore the feasibility of applying a nonlinear adaptive controller employing NN as feedforward, augmented with a continuous robust integral of the signum of the error (RISE) term connected as feedback in order to improve the performance of the degraded system. Typically NN based adaptive controller guarantees only uniformly ultimately bounded stability while the suggested control system assures semi-global asymptotic tracking of the missile. In order to accomplish the adaptive behavior, the neural network is passed through learning stage to update the weight matrices and gains by using the adaptation rules that are derived from the Lyapunov stability techniques. Results of the simulations of the proposed algorithm on six degree of freedom nonlinear missile validates feasibility of the control law. The result of the proposed controller are compared with results obtained using the backstepping technique in this paper.

This paper presents design, simulation and fabrication of a surface electromyographic (SEMG) sensor for control of prosthetic devices. EMG activity is mainly the generation of a bio-potential signal (electrical signals) due to muscle action. These signals picked from motor points of muscles are contaminated with various intrinsic/extrinsic noises, which must be removed through different filtering techniques in order to develop a sensor that has a high signal-to-noise ratio. Power spectral density (PSD) of any EMG signal plays a vital role to determine the signal strength. A novel Simulink model has been developed which mimics various elements of an active SEMG sensor. By using this model, low/high/notch filters are designed and optimized. The model is also used to simulate the effects of these filters on power spectral density (PSD) of the EMG signal. Simulation of double rectification and smoothing (envelopment) is also carried out. EMG signals recorded from the Tibialis anterior, monopolar needle, and fine wire isometric contraction were used in this simulation. Finally, on the basis of simulation results, instrumentation of surface EMG sensor is designed and fabricated. Performance/results of developed SEMG sensor are in accordance with the simulation results of the developed Simulink model.