Satisfying safety constraints is a priority concern when solving optimal control problems (OCPs). Due to the existence of infeasibility phenomenon, where a constraint-satisfying solution cannot be found, it is necessary to identify a feasible region before implementing a policy. Existing feasibility theories built for model predictive control (MPC) only consider the feasibility of optimal policy. However, reinforcement learning (RL), as another important control method, solves the optimal policy in an iterative manner, which comes with a series of non-optimal intermediate policies. Feasibility analysis of these non-optimal policies is also necessary for iteratively improving constraint satisfaction; but that is not available under existing MPC feasibility theories. This paper proposes a feasibility theory that applies to both MPC and RL by filling in the missing part of feasibility analysis for an arbitrary policy. The basis of our theory is to decouple policy solving and implementation into two temporal domains: virtual-time domain and real-time domain. This allows us to separately define initial and endless, state and policy feasibility, and their corresponding feasible regions. Based on these definitions, we analyze the containment relationships between different feasible regions, which enables us to describe the feasible region of an arbitrary policy. We further provide virtual-time constraint design rules along with a practical design tool called feasibility function that helps to achieve the maximum feasible region. We review most of existing constraint formulations and point out that they are essentially applications of feasibility functions in different forms. We demonstrate our feasibility theory by visualizing different feasible regions under both MPC and RL policies in an emergency braking control task.
In recent years, the control theory and automation science communities have witnessed significant advances in the field of networked control systems, where communication between sensors, actuators, and controllers occurs over a shared digital communication network. In networked control systems, the efficient utilization of communication resources has become a critical issue due to limitations such as the restricted communication bandwidth and limited energy available from onboard batteries. As a resource-efficient control strategy, event-triggered control has garnered increasing attention from researchers in the field of networked control systems. By constructing a closed-loop connection between the realtime system behavior and transmission decisions, event-triggered control effectively balances system performance with resource consumption. This monograph reviews the fundamental concepts and recent progress in event-triggered networked control for continuous-time deterministic systems. It begins with a brief introduction to the foundational setups of networked and event-triggered control systems. The discussion then explores several widely used event-triggered control strategies, providing a comprehensive overview of their various event-triggering conditions, operating mechanisms, and the respective advantages and disadvantages of each. Next, two primary methods employed in the analysis and design of event-triggered control systems are presented: the emulation-based approach and the co-design approach. Finally, the monograph highlights recent advances in the analysis and design of event-triggered networked control systems, with particular emphasis on adapting event-triggering conditions to accommodate diverse scenarios involving specific performance objectives and network-induced imperfections.
Distributed computing seeks to solve global problems without a central coordinator, for physically decentralized agents holding local and private data over a communication network. This monograph provides an overview of continuous flows as distributed solvers for linear algebraic equations, linear matrix equations, constrained convex optimization, and Nash equilibrium seeking, highlighting the interface between graph theory, control systems, and optimization.
Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve many interacting parameters, yet it is crucial for explaining processes from cellular regulation to disease onset and epidemic spreading. Robustness and resilience describe a system's ability to preserve and recover desired behaviours in the presence of intrinsic and extrinsic fluctuations. This survey reviews how different disciplines define these concepts, examines methods for assessing whether key properties of uncertain, networked dynamical systems are structural (parameter-free) or robust (preserved for parameter variations within an uncertainty bounding set), and discusses integrated structural and probabilistic techniques for biological and epidemiological models. The text introduces formal definitions of resilience for families of systems obtained by adding stochastic perturbations to a nominal deterministic model, enabling a probabilistic characterisation of the ability to remain within or return to a prescribed attractor. These definitions generalise probabilistic robustness and shed new light on classical biological examples. In addition, the survey summarises resilience indicators and data-driven tools for detecting resilience loss and regime shifts, drawing on bifurcation analysis to anticipate qualitative changes in system behaviour. Together, these methodologies support the study and control of complex natural systems, guiding the design of biomolecular feedback architectures, the identification of therapeutic targets, the forecasting and management of epidemics, and the detection of tipping points in ecological and biological networks.
This monograph presents for the first time a unified synthesis on how to design robust and predictive control approaches for (discrete-time) Linear Parameter Varying (LPV) systems. In particular, some recent results concerning LPV state feedback design using the H-infinity framework and Model Predictive Control (MPC) for LPV systems are presented. Then, both approaches are illustrated in two important cases for automotive applications. First, the lateral steering control of autonomous vehicles is considered. Then, an application to Advanced Driver-Assistance Systems is presented, where MPC and LPV approaches are integrated in view of optimal selection of the scheduling parameter.
