ABSTRACT This paper proposes a novel dynamic terminal set approach for the model predictive control (MPC) design. It concerns the class of linear systems subject to stochastic disturbances and builds upon an indirect feedback (IF) strategy. The main contribution is to explore the time‐varying definition of the constraints in the indirect feedback SMPC (IF‐SMPC) to improve the feasible domain. Using this feature, the closed‐loop performance of the indirect SMPC is not degraded, and the domain of attraction is enlarged, while the number of decision variables of the SMPC optimization problem is preserved. A constructive procedure is provided to obtain the sequence of time‐varying (evolving) terminal sets. Moreover, simulation case studies based on two benchmarks illustrate the notions and show the advantage of the new time‐varying terminal set approach for the IF‐SMPC.

A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both a reference governor for the bottom layer and as a feedback controller for the regulated network. By employing set-based methods, global theoretical guarantees are obtained by enforcing local constraints upon the network's variables and upon those of the first layer's implementation. The proposed technique offers recursive feasibility guarantees as one of its central features, and the expressions of the resulting predictive strategies bear a striking resemblance to classical formulations from model predictive control literature, allowing for flexible and easily customisable implementations. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

The paper concentrates on the analysis of the Region of Attraction (RoA) for unknown autonomous dynamical systems. The aim is to explore a data-driven approach based on moment Sum-of-Squares (SoS) hierarchy, which enables novel RoA outer approximations despite the reduced information on the structure of the dynamics. The main contribution of this work is bypassing the system model and, consequently, the recurring constraint on its polynomial structure. Numerical experimentation showcases the influence of data on learned approximating sets, offering a promising outlook on the potential of this method.

This paper extends the recently proposed dynamic model for local energy markets (LEM) by introducing a control-based formulation that ensures faster convergence and improved transient performance. The original model captures the interactions between producers and consumers in LEMs through monotonic and bijective supply and demand functions, leading to a unique market-clearing price (MCP) as a global attractor. However, asymmetric behavior of price and quantity dynamics can result in oscillations and slow convergence. To overcome these limitations, we propose a control law that preserves the equilibrium while reshaping the transient response. Analytical conditions are presented, providing sufficient guarantees of global convergence. Numerical results demonstrate that the proposed controller effectively damps oscillations, accelerates convergence, and maintains the autonomy properties of the original model, making it a promising approach for the dynamic coordination of LEMs.

This paper proposes a dynamic market-based formulation for computing the market-clearing price (MCP) in bipartite local energy markets (LEMs). Unlike conventional distributed optimization approaches, the proposed framework is derived from a direct market-theoretic interpretation of producer and consumer behavior under competitive assumptions. By removing structural redundancies inherent to bilateral optimization-based formulations, the model reduces the number of state variables by up to 75% in large-scale settings, thereby improving scalability while preserving participant autonomy and privacy. A theoretical analysis, based on Lyapunov stability and LaSalle’s invariance principle, guarantees global convergence to a unique MCP and equilibrium quantity. Numerical simulations demonstrate improved convergence behavior compared to representative ADMM and dual decomposition mechanisms, particularly as the number of participants increases. Furthermore, the framework accommodates nonlinear willingness functions without increasing structural complexity, enabling a more varied representation of heterogeneous flexibility in supply and demand. These findings show that market equilibrium in decentralized LEMs can be characterized as a globally stable dynamic system, enabling scalable pricing mechanisms without relying on high-dimensional distributed optimization formulations.

A two-layer control architecture is proposed to enable scalable implementations for constraintbased decision strategies, such as model predictive controllers. The bottom layer is based upon a distributed feedback-feedforward scheme that directs the controlled network's information flow according to a pre-specified communication infrastructure. Explicit expressions for the resulting closedloop maps are obtained, and an offline model-matching procedure is proposed for designing the first layer. The obtained control laws are deployed via distributed state-space-based implementations, and the resulting closed-loop models enable predictive control design for the constraint management procedure described in our companion paper. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper presents a reactive path planning framework based on convex lifting for safe navigation in dynamic environments. The framework employs an iterative selective path planning strategy, in which a new candidate path is generated at each time step and updated (guaranteeing improvements by direct or indirect comparison with the previous one). A novel method, termed set-interpolation, is then introduced to adaptively enlarge obstacles within the convex-lifting generated partition. This mechanism allows flexible evolution of paths farther from the agent while conserving the path near the agent. The enlargement process effectively creates a dynamic buffer zone that shifts the agent’s safe partition away from obstacle boundaries, thereby enhancing safety in real-time operation. The proposed framework is evaluated in a time-varying environment with multiple moving obstacles.

Congestion challenges within power transmission networks are escalating due to the growing integration of renewable energy sources. Transmission system operators (TSOs) traditionally address these issues through network reconfiguration or by limiting the power generated from renewables in complex subtransmission areas. However, there is an increasing need for sophisticated methodological tools that empower operators to more efficiently manage optimal power flow. This entails exploring innovative solutions, including the integration of storage devices alongside curtailment strategies. In response to this demand, our article introduces mathematical models and numerical tools designed to facilitate the partial curtailment of renewable power. These models are presented as dynamic systems, offering a comprehensive depiction of the transmission network and accommodating the presence of storage devices. They are then employed within a model-based receding horizon control approach. Finally, these models are implemented in an open-source tool that facilitates the application of the proposed control strategies in realistic simulations based on MATPOWER.

This paper proposes a constraint-switching approach for Nonlinear Model Predictive Control (NMPC) to address the challenges of large prediction horizons coupled with recursively feasible constraints in particular for design frameworks which imply exploration goals.The K-invariant pairs and their parameterization are introduced as a substitute for controlled invariant sets. It is shown that such sets can be effectively constructed through an external selection and verification module, making them available along the prediction horizon. The availability of K-invariant pairs and their enforcement as constraints in the receding optimization for exploration purposes lead to a switching mechanism for the predictive control.Recursive feasibility is guaranteed under the framework, and an example of navigation in a partially known environment is provided to demonstrate its advantages.

This paper presents a method to approximate regions of attraction of unknown nonlinear dynamical systems from data. Assuming point-wise evaluations of the vector field and known Lipschitz bounds, a polyhedral uncertainty set of admissible dynamics is constructed. This uncertainty description enables the synthesis of a continuous PWA Lyapunov candidate via a linear program, enforcing a robust decrease condition for all admissible vector fields. The approach allows certification of a region of attraction consistent with the available data. Numerical examples illustrate the effectiveness of the proposed method in extracting certified regions of attraction from sparse data.

This paper presents a library-free, approximated Model Predictive Control (MPC) for systems with fast dynamics and limited computational resources. Conventional MPC relies on optimisation solvers, which can be computationally demanding and often require commercial solver licenses, making them less suitable for embedded systems. The proposed approach replaces solvers with a procedure that randomly samples a set of control sequences. The samples are evaluated for primal feasibility, and the best-performing suboptimal sequence is applied. Two improvements, variance-decaying and variance-adaptive approximated MPC, are introduced to direct the sampling procedure toward promising regions of the feasible solution space by sampling from a multivariate normal distribution. The variance-adaptive approximate MPC is designed to increase response to disturbances. Another advantage is the predictable and bounded computational effort, as the number of samples per control iteration can be directly conditioned by the available sampling time. Closed-loop stability and recursive feasibility are ensured through an auxiliary support controller. The resulting method remains solver-free, lightweight, and suitable for embedded implementations, while offering tunable performance–complexity trade-offs. Validation on a multivariable quadrotor model shows reliable control performance even under disturbances, and real-time experiments on Flexy2 PC–Arduino setup confirm its robustness on physical hardware.

A novel set-theoretical approach to hands-off control is proposed, which focuses on spatial arguments for command limitation, rather than temporal ones. By employing dynamical feedback alongside invariant set-based constraints, actuation is employed only to drive the system’s state inside a “hands-off region” of its state-space, where the plant may freely evolve in open-loop configuration. A computationally-efficient procedure with strong theoretical guarantees is devised, and its effectiveness is showcased via an intuitive practical example.

The prediction mechanism for energy storage systems-such as state of charge, capacity, or end-of-discharge points-is improved by online adapting model parameters using available measurements, thereby enhancing overall accuracy. However, this online adaptation is subject to uncertainties and disturbances and involves filtering and estimation techniques that come with a nonnegligible computational load and have to be fine-tuned in order to meet the real-time constraints. On top of these challenges, the ultimate objective of the model adaptation is twofold: first, the monitoring and diagnosis for a safe use and, second, an operational adjustment of the discharge profile to meet both performance optimization and constraints satisfaction. While the diagnosis relies on open-loop supervision techniques based on adequate residual generation, the operational optimization can be efficiently achieved by means of a receding horizon control strategy. The present paper reviews all these principles and their practical implementation for a trielectrode zinc-air cell constructed in a laboratory-based infrastructure.

In this paper, we revisit the path planning approach based on convex lifting and extend it to accommodate non-convex obstacles. Obstacles are modeled as overlapping unions of polyhedra. To handle complex environments, a preprocessing module is required to reconstruct the obstacles, and convex lifting is used to obtain an interconnected graph. A post-processing module will then remove graph edges that intersect obstacles, thereby extracting only feasible paths. We propose two obstacle representations that are compatible with the convex lifting framework, significantly broadening its applicability. Furthermore, we address the potential loss of connectivity resulting from the removal of obstacle-intersecting edges and propose a solution to maintain connectivity and thus ensure the preservation of collision-free paths.

This paper presents a novel and integrated framework for motion planning and control in time-varying environments. The proposed method combines a time-parameterized convex-lifting-based path planning approach—including state space partitioning, graph generation, pathfinding, and safe corridor generation—with a spatiotemporal formulation to guide motion planning. To ensure dynamic feasibility, the framework is extended with a Model Predictive Control (MPC) scheme that computes safe trajectories within the identified corridors. A replanning strategy is introduced to adapt to the unpredictable behaviors of surrounding vehicles and maintain the feasibility of trajectories. Simulation results in an overtaking scenario demonstrate the effectiveness of the approach, with the ego vehicle successfully performing trajectory tracking and replanning while satisfying dynamic constraints.

Tube-based Model Predictive Control (MPC) is a widely adopted robust control framework for constrained linear systems under additive disturbance. The paper is focused on reducing the numerical complexity associated with the tube parameterization, described as a sequence of elastically-scaled zonotopic sets. A new class of scaled-zonotope inclusion conditions is proposed, alleviating the need for a priori specification of certain set-containment constraints and achieving significant reductions in complexity. A comprehensive complexity analysis is provided for both the polyhedral and the zonotopic setting, illustrating the trade-off between an enlarged domain of attraction and the required computational effort. The proposed approach is validated through extensive numerical experiments.

This paper presents a solution to an on-ramp merging trajectory planning problem within a multiple target vehicles environment by employing model predictive control principles. The shrinking horizon MPC (SHMPC) scheme is used to guarantee that the optimal trajectories are selected among the available gaps into which the ego vehicle can merge. For each trajectory, a time-varying terminal set is used to ensure recursive feasibility and to fulfill the safety and obstacle avoidance constraints. To enhance computational efficiency, a procedure is proposed for defining the terminal set to be as large as possible, derived from the offline-calculated maximum controlled invariant set. We present a simple decision mechanism, accounting for safety, comfort, and efficiency. Then, we demonstrate the effectiveness of the proposed solution by applying it to two different scenarios.

This article deals with the fragility margins of discrete-time piecewise affine (PWA) closed-loop dynamics. The chosen framework is one of the nominal linear systems in closed-loop with a PWA controller implemented using a binary search tree mechanism for effective gain selection. Our objective is to preserve the properties of nominal dynamics, particularly the positive invariance under perturbations in the control law representation. The main contribution revolves around defining and constructing two distinct types of fragility margins: the single hyperplane fragility margin (sHFM) and the multiple hyperplane fragility margin (mHFM). The sHFM specifically examines the admissible perturbations for a single hyperplane defining the nominal PWA controller's partition. In contrast, the mHFM explores the admissible perturbations for multiple hyperplanes simultaneously, and the perturbed multiple hyperplanes need to adapt special operations to decouple the influence between each hyperplane. This margin exhibits the extent of freedom for perturbations across multiple hyperplanes simultaneously.

In this paper, an approach to automatic tuning of suboptimal distributed MPC (DMPC) of linear interconnected systems with coupled dynamics subject to both state and input constraints is proposed. The purpose is to obtain a desired closed-loop performance without exceeding a limit on the online computational complexity. The approach includes three stages which are performed offline. First, the optimal tuning of the MPC cost function parameters is obtained for different values of the suboptimal DMPC design parameters by adjusting the DMPC closed-loop performance. Then, a neural network is used to approximate the influence of the design parameters on the performance and the computational complexity. As a third stage, the best choice of the design parameters is determined by solving an optimization problem based on the obtained neural network model. The suggested approach would be appropriate for embedded distributed MPC since it will reduce the complexity of the online MPC computations and simplify the software implementation. (C) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)