We consider supervisory control of nonlinear systems which are implemented on digital networks. In particular, two candidate controllers are orchestrated by a supervisor to stabilize the origin of the plant by following a dwell time logic, i.e. evaluating a control-mode switching rule at instants which are at least spaced by some dwell time interval. The plant, the controllers and the supervisor communicate via a network and the transmissions are triggered by a mechanism at the discrete sampling instants, which leads to periodic event-triggered control. Thus, there are possibly two kinds of events generated at the sampling instants: the control-mode switching event to activate another control law and the transmission event to update the control input. We propose a systematic design procedure for periodic event-triggered supervisory control for nonlinear systems. We start from a supervisory control scheme which robustly stabilizes the system in the absence of the network. We then implement it over the network and design event-triggering rules to preserve its stability properties. In particular, for each candidate controller, we provide a lower bound for the control-mode dwell time, design criterion to generate transmission events and present an explicit bound on the maximum sampling period with which the triggering rules are evaluated, to ensure stability of the whole system. We show that there exist relationships among the control-mode dwell time, a parameter used to define the transmission event-triggering condition and the bound of the sampling period. An example is given to illustrate the results.

A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with hybrid dynamical systems analysis techniques. In the rich literature regarding this framework, various bounds on the maximal allowable transmission interval (MATI) are provided to guarantee stability properties of the NCS using Lyapunov-based arguments for hybrid systems. In this work, we provide a generalization of these Lyapunov-based proofs, showing how the existing results for the MATI can be improved by only considering a different, more general hybrid Lyapunov function, while not altering the conditions in the analysis itself.

Estimation of physical variables of nonlinear systems with two-time scales is a hard task to address. Whilst nonlinear systems exhibiting a singularly perturbed structure are common in engineering applications, current observer design results apply only to a specific class of plants and observers. We consider a broader class of plants and observers to generalise existing results on observer design for slow states of nonlinear singularly perturbed systems. Under reasonable assumptions, it is shown that the estimation error can be made semi-globally practically asymptotically stable in the singular perturbation parameter. This subsequently leads to appropriate conditions for the observer design for slow variables that guarantee satisfactory estimation error performance in the full system.

A secure nonlinear networked control system (NCS) design using semi-homomorphic encryption, namely, Paillier encryption is studied. Under certain assumptions, control signal computation using encrypted signal directly is allowed by semi-homomorphic encryption. Thus, the security of the NCSs is further enhanced by concealing information on the controller side. However, additional technical difficulties in the design and analysis of NCSs are induced compared to standard NCSs. In this paper, the stabilization of a nonlinear discrete time NCS is considered. More specifically, sufficient conditions on the encryption parameters that guarantee stability of the NCS are provided, and a trade-off between the encryption parameters and the ultimate bound of the state is shown.

We investigate the stabilization of perturbed nonlinear systems using output-based periodic event-triggered controllers. Thus, the communication between the plant and the controller is triggered by a mechanism, which evaluates an output- and input-dependent rule at given sampling instants. We address the problem by emulation. Hence, we assume the knowledge of a continuous-time output feedback controller, which robustly stabilizes the system in the absence of network. We then implement the controller over the network and model the overall system as a hybrid system. We design the event-triggered mechanism to ensure an input-to-state stability property. An explicit bound on the maximum allowable sampling period at which the triggering rule is evaluated is provided. The analysis relies on the construction of a novel hybrid Lyapunov function. The results are applied to a class of Lipschitz nonlinear systems, for which we formulate the required conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.

Discounted costs are considered in many fields, like reinforcement learning, for which various algorithms can be used to obtain optimal inputs for finite horizons. The related literature mostly concentrates on optimality and largely ignores stability. In this context, we study stability of general nonlinear discrete- time systems controlled by an optimal sequence of inputs that minimizes a finite-horizon discounted cost computed in a receding horizon fashion. Assumptions are made related to the stabilizability of the system and its detectability with respect to the stage cost. Then, a Lyapunov function for the closed-loop system with the receding horizon controller is constructed and a uniform semiglobal stability property is ensured, where the adjustable parameters are both the discount factor and the horizon length. Uniform global exponential stability is guaranteed by strengthening the initial assumptions, in which case explicit bounds on the discount factor and the horizon length are provided. We compare the obtained bounds in the particular cases where there is no discount or the horizon is infinite, respectively, with related results in the literature and we show our bounds improve existing ones on the examples considered.

We address the problem of state estimation, attack isolation, and control for discrete-time Linear Time Invariant (LTI) systems under (potentially unbounded) actuator false data injection attacks. Using a bank of Unknown Input Observers (UIOs), each observer leading to an exponentially stable estimation error in the attack-free case, we propose an estimator that provides exponential estimates of the system state and the attack signals when a sufficiently small number of actuators are attacked. We use these estimates to control the system and isolate actuator attacks. Simulations results are presented to illustrate the performance of the results.

In this note, we study the stability of the error dynamics of an observer designed to estimate only the slow states of a singularly perturbed system. The observer is designed on the basis of the reduced (slow) model. We have recently reported semi-global practical results for this problem. Our previous work can be used to state local and regional convergence of the estimation error, but we cannot conclude global results from it. We seek to prove a stronger (global) result under stronger (global) assumptions in this manuscript. Moreover, we focus on proving the robustness of an observer with respect to singular perturbations and with respect to the measurement noise.

Many industrial domains are characterized by Multiple-Input-Multiple-Output (MIMO) systems for which an explicit relationship capturing the nontrivial trade-off between the competing objectives is not available. Human experts have the ability to implicitly learn such a relationship, which in turn enables them to tune the corresponding controller to achieve the desirable closed-loop performance. However, as the complexity of the MIMO system and/or the controller increase, so does the tuning time and the associated tuning cost. To reduce the tuning cost, a framework is proposed in which a machine learning method for approximating the human-learned cost function along with an optimization algorithm for optimizing it, and consequently tuning the controller, are employed. In this work the focus is on the tuning of Model Predictive Controllers (MPCs), given both the interest in their implementations across many industrial domains and the associated high degrees of freedom present in the corresponding tuning process. To demonstrate the proposed approach, simulation results for the tuning of an air path MPC controller in a diesel engine are presented.

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order $\mathcal{O} (\sqrt{\varepsilon})$, where $\varepsilon$ is the perturbation parameter.

We study the problem of maximizing privacy of quantized sensor measurements by adding random variables. In particular, we consider the setting where information about the state of a process is obtained using noisy sensor measurements. This information is quantized and sent to a remote station through an unsecured communication network. It is desired to keep the state of the process private; however, because the network is not secure, adversaries might have access to sensor information, which could be used to estimate the process state. To avoid an accurate state estimation, we add random numbers to the quantized sensor measurements and send the sum to the remote station instead. The distribution of these random variables is designed to minimize the mutual information between the sum and the quantized sensor measurements for a desired level of distortion - how different the sum and the quantized sensor measurements are allowed to be. Simulations are presented to illustrate our results.

As more attention is paid to security in the context of control systems and as attacks occur to real control systems throughout the world, it has become clear that some of the most nefarious attacks are those that evade detection. The term stealthy has come to encompass a variety of techniques that attackers can employ to avoid being detected. In this manuscript, for a class of perturbed linear time-invariant systems, we propose two security metrics to quantify the potential impact that stealthy attacks could have on the system dynamics by tampering with sensor measurements. We provide analysis mathematical tools (in terms of linear matrix inequalities) to quantify these metrics for given system dynamics, control structure, system monitor, and set of sensors being attacked. Then, we provide synthesis tools (in terms of semidefinite programs) to redesign controllers and monitors such that the impact of stealthy attacks is minimized and the required attack-free system performance is guaranteed.

Recent developments in computer and communication technologies are leading to an increasingly networked and wireless world. This raises new challenging questions in the context of networked control systems, especially when the computation, communication and energy resources of the system are limited. To efficiently use the available resources it is desirable to limit the control actions to instances when the system really needs attention. Unfortunately, the classical time-triggered control paradigm is based on performing sensing and actuation actions periodically in time (irrespective of the state of the system) rather than when the system needs attention. Therefore, it is of interest to consider event-triggered control as an alternative paradigm as it is more natural to trigger control actions based on the system state, output, or other available information. Event-triggered control can thus be seen as the introduction of feedback in the sensing, communication, and actuation processes. To facilitate an easy implementation of event-triggered control, we propose to combine the principles and particularly the benefits of event-triggered control and classical periodic time-triggered control. The idea is to periodically evaluate the triggering condition and to decide, at every sampling instant, whether the feedback loop needs to be closed. This leads to the so-called periodic event-triggered control (PETC) systems. In this chapter, we discuss PETC strategies, their benefits and two analysis and design frameworks for linear and nonlinear plants, respectively.