We address the problem of state estimation, attack isolation, and control of discrete-time linear time-invariant systems under (potentially unbounded) actuator and sensor false data injection attacks. Using a bank of unknown input observers, each observer leading to an exponentially stable estimation error (in the attack-free case), we propose an observer-based estimator that provides exponential estimates of the system state despite actuator and sensor attacks. Exploiting sensor and actuator redundancy, the estimation scheme is guaranteed to work if a sufficiently small subset of sensors and actuators is under attack. Using the proposed estimator, we provide tools for reconstructing and isolating actuator and sensor attacks, and a control scheme capable of stabilizing the closed-loop dynamics by switching off isolated actuators. Simulation results are presented to illustrate the performance of our tools.

It is well-known that for a class of minimum-phase relative degree one linear-time-invariant (LTI) systems, with a unit feedback control structure, overshoot necessarily happens if the plant transfer function has poles at origin or unstable poles. This work aims to overcome this overshoot performance limitation (OPL) by using a novel reset controller, which has a generalized first order reset element (GFORE) structure. By tuning parameters of this reset controller carefully, the non-overshoot performance can be ensured. Furthermore, the implementation of the proposed reset controller with a high-pass filter is provided. Parameter tuning guidelines are also provided and, finally, the proposed design is verified with a simulation example.

A major challenge in atomic force microscopy is to reduce the scan duration while retaining the image quality. Conventionally, the scan rate is restricted to a sufficiently small value in order to ensure a desirable image quality as well as a safe tip–sample contact force. This usually results in a conservative scan rate for samples that have a large variation in aspect ratio and/or for scan patterns that have a varying linear velocity. In this paper, an adaptive scan scheme is proposed to alleviate this problem. A scan line-based performance metric balancing both imaging speed and accuracy is proposed, and the scan rate is adapted such that the metric is optimized online in the presence of aspect ratio and/or linear velocity variations. The online optimization is achieved using an extremum-seeking approach, and a semiglobal practical asymptotic stability result is shown for the overall system. Finally, the proposed scheme is demonstrated via both simulation and experiment.

In preference learning, it is beneficial to incorporate monotonicity constraints for learning utility functions when there is prior knowledge of monotonicity. We present a novel method for learning utility functions with monotonicity constraints using Gaussian process regression. Data is provided in the form of pairwise comparisons between items. Using conditions on monotonicity for the predictive function, an algorithm is proposed which uses the weighted average between prior linear and maximum a posteriori (MAP) utility estimates. This algorithm is formally shown to guarantee monotonicity of the learned utility function in the dimensions desired. The algorithm is tested in a Monte Carlo simulation case study, in which the results suggest that the learned utility by the proposed algorithm performs better in prediction than the standalone linear estimate, and enforces monotonicity unlike the MAP estimate.

We study the design of state observers for nonlinear networked control systems (NCSs) that are implemented over WirelessHART (WH). WH is a wireless communication protocol for process automation applications. It is characterised by its multi-hop structure, slotted communication cycles, and simultaneous transmission over different frequencies. We present a solution based on the emulation approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a WH network and we provide sufficient conditions on the latter, to preserve the stability property of the observer. In particular, we provide explicit bounds on the maximum allowable transmission interval. We assume that the plant dynamics and measurements are affected by noise and we guarantee an input-to-state stability property for the corresponding estimation error system.

Many natural and engineered systems exhibit a singularly perturbed structure where different time scales inherently lead to difficulties in the design of observers for the system. In our related work [1], we have shown that, under appropriate assumptions, an observer designed for the slow part of the system can be applied and results in semi-global practical asymptotical (SPA) stability of the estimation error. In this paper, we show that assumptions from [1] hold for two classes of plants and nonlinear observers. In fact, we show that the provided framework in [1] covers current results in the literature and also other cases that are not covered by existing results. Hence, we demonstrate that we generalise existing results in the literature.

This paper presents an analytical framework to design and analyze hybrid extremum seeking controllers for plants with hybrid dynamics. The extremum seeking controllers are characterized by a hybrid dither generator, a hybrid Jacobian estimator, and a hybrid dynamic optimizer. This structure allows us to consider a family of novel extremum seeking controllers that have not been studied in the literature before. Moreover, the hybrid extremum seeking controllers can be applied to plants with hybrid dynamics generating well-defined response maps. A convergence result is established for the closed -loop system by using singular perturbation theory for hybrid dynamical systems with hybrid boundary layers.

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.