We present an event-triggered observer design for linear time-invariant systems, where the measured output is sent to the observer only when a triggering condition is satisfied. We proceed by emulation and we first construct a continuous-time Luenberger observer. We then propose a dynamic rule to trigger transmissions, which only depends on the plant output and an auxiliary scalar state variable. The overall system is modeled as a hybrid system, for which a jump corresponds to an output transmission. We show that the proposed event-triggered observer guarantees global practical asymptotic stability for the estimation error dynamics. Moreover, under mild boundedness conditions on the plant state and its input, we prove that there exists a uniform strictly positive minimum inter-event time between any two consecutive transmissions, guaranteeing that the system does not exhibit Zeno solutions. Finally, the proposed approach is applied to a numerical case study of a lithium-ion battery.

Cooperative Adaptive Cruise Control (CACC) is a vehicular technology that allows groups of vehicles on the highway to form in closely-coupled automated platoons to increase highway capacity and safety. The underlying mechanism behind CACC is the use of Vehicle-to-Vehicle (V2V) wireless communication networks to transmit acceleration commands to adjacent vehicles in the platoon. However, the use of V2V networks leads to increased vulnerabilities against faults and cyberattacks. Here, we address the problem of increasing the robustness of CACC schemes against cyberattacks by using multiple V2V networks and a data fusion algorithm. The idea is to transmit acceleration commands multiple times through different communication channels to create redundancy at the receiver side. We propose a data fusion algorithm to estimate of the true acceleration command, and isolate compromised channels. Finally, we propose a robust $H_{\infty }$ controller that reduces the joint effect of fusion errors and sensor/channel noise in the platooning performance (tracking performance and string stability). Simulation results are presented to illustrate the performance of our approach.

Originating in the artificial intelligence literature, optimistic planning (OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is, therefore, relevant for the near-optimal control of nonlinear switched systems for which the switching signal is the control, and no continuous input is present. However, OP exhibits several limitations, which prevent its desired application in a standard control engineering context, as it requires, for instance, that the stage cost takes values in <inline-formula><tex-math notation="LaTeX">$[0, 1]$</tex-math></inline-formula>, an unnatural prerequisite, and that the cost function is discounted. In this article, we modify OP to overcome these limitations, and we call the new algorithm <inline-formula><tex-math notation="LaTeX">${\rm OP}_{\text{min}}$</tex-math></inline-formula>. We then analyze <inline-formula><tex-math notation="LaTeX">${\rm OP}_{\text{min}}$</tex-math></inline-formula> under general stabilizability and detectability assumptions on the system and the stage cost. New near-optimality and performance guarantees for <inline-formula><tex-math notation="LaTeX">${\rm OP}_{\text{min}}$</tex-math></inline-formula> are derived, which have major advantages compared to those originally given for OP. We also prove that a system whose inputs are generated by <inline-formula><tex-math notation="LaTeX">${\rm OP}_{\text{min}}$</tex-math></inline-formula> in a receding-horizon fashion exhibits stability properties. As a result, <inline-formula><tex-math notation="LaTeX">${\rm OP}_{\text{min}}$</tex-math></inline-formula> provides a new tool for the near-optimal, stable control of nonlinear switched discrete-time systems for generic cost functions.

We address the problem of robust state reconstruction for discrete-time nonlinear systems when the actuators and sensors are injected with (potentially unbounded) attack signals. Exploiting redundancy in sensors and actuators and using a bank of unknown input observers (UIOs), we propose an observer-based estimator capable of providing asymptotic estimates of the system state and attack signals under the condition that the numbers of sensors and actuators under attack are sufficiently small. Using the proposed estimator, we provide methods for isolating the compromised actuators and sensors. Numerical examples are provided to demonstrate the effectiveness of our methods.

We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chance-constrained program which has black-box functions. The algorithm leverages ideas from the areas of randomised algorithms and ordinal optimisation, and also draws comparisons with the scenario approach; these have all been previously applied to finding approximate solutions for difficult design problems. By exploiting statistical correlations through black-box sampling, we formally prove that our algorithm yields a controller meeting the prescribed probabilistic performance specification. Additionally, we characterise the computational requirement of the algorithm with a probabilistic lower bound on the algorithm's stopping time. To validate our work, the algorithm is then demonstrated for tuning model predictive controllers on a diesel engine air-path across a fleet of vehicles. The algorithm successfully tuned a single controller to meet a desired tracking error performance, even in the presence of the plant uncertainty inherent across the fleet. Moreover, the algorithm was shown to exhibit a sample complexity comparable to the scenario approach.

In this article, we study the problem of minimizing the sum of potentially nondifferentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the behavior of an asynchronous algorithm based on dual decomposition and block coordinate subgradient methods under assumptions weaker than those used in the literature. At the same time, we allow different agents to use local stepsizes with no global coordination. Sufficient conditions are provided for almost sure convergence to the solution of the optimization problem. Under additional assumptions, we establish a sublinear convergence rate that, in turn, can be strengthened to the linear convergence rate if the problem is strongly convex and has Lipschitz gradients. We also extend available results in the literature by allowing multiple and potentially overlapping blocks to be updated at the same time with nonuniform and potentially time-varying probabilities assigned to different blocks. A numerical example is provided to illustrate the effectiveness of the algorithm.

Minimum attention control proposed by Brockett is an important formulation for resource-aware control, while his problem formulation and the underlying optimization problem that he proposed is in general very hard. In this paper, we propose a computationally tractable design method of minimum attention control based on promoting sparsity of the derivative of control. The optimal control problem is formulated as L0 norm minimization of the time derivative of control under the constraint that the derivative is bounded by a fixed value. This is a non-convex problem, and we propose L1 relaxation for linear systems to obtain optimal control by efficient numerical computation. We then show equivalence theorems between the L0 and L1 optimal controls. Also, we present an example of feedback control for the first-order integrator, that illustrates the proposed methodology.

We propose a unifying emulation-based design framework for the event-triggered control of nonlinear systems that is based on a hybrid small-gain perspective. We show that various existing event-triggered controllers fit the unifying perspective. Moreover, we demonstrate that the flexibility offered by our approach can be used for the development of novel event-triggered schemes and for a systematic modification and improvement of existing schemes. Finally, we illustrate via a simulation example that these novel and/or modified event-triggered controllers can lead to a reduction in the required number of transmissions, while still guaranteeing the same stability properties.

This paper studies the behaviour of observers for the slow states of a general singularly perturbed system – that is a singularly perturbed system which has boundary-layer solutions that do not necessarily converge to a slow manifold. The solutions of the boundary-layer system are allowed to exhibit persistent (e.g. oscillatory) steady-state behaviour which are averaged to obtain the dynamics of the approximate slow system. It is shown that if an observer has certain properties such as asymptotic stability of its error dynamics on average, then it is practically asymptotically stable for the original singularly perturbed system.

We study emulation-based stabilisation of nonlinear networked control systems communicating over multiple wireless channels subject to packet loss. Specifically, we establish sufficient conditions on the rate of transmission that guarantee ℒp stability-in-expectation of the overall closed-loop system. These conditions depend on the cumulative dropout probability of the network nodes for static protocols. We use the obtained stability results to study power control, where we show there are interesting trade-offs between the transmission rate, transmit power, and stability. Lastly, numerical examples are presented to illustrate our results.

Value iteration (VI) is a ubiquitous algorithm for optimal control, planning, and reinforcement learning schemes. Under the right assumptions, VI is a vital tool to generate inputs with desirable properties for the controlled system, like optimality and Lyapunov stability. As VI usually requires an infinite number of iterations to solve general nonlinear optimal control problems, a key question is when to terminate the algorithm to produce a "good" solution, with a measurable impact on optimality and stability guarantees. By carefully analysing VI under general stabilizability and detectability properties, we provide explicit and novel relationships of the stopping criterion's impact on near-optimality, stability and performance, thus allowing to tune these desirable properties against the induced computational cost. The considered class of stopping criteria encompasses those encountered in the control, dynamic programming and reinforcement learning literature and it allows considering new ones, which may be useful to further reduce the computational cost while endowing and satisfying stability and near-optimality properties. We therefore lay a foundation to endow machine learning schemes based on VI with stability and performance guarantees, while reducing computational complexity.

We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant cases. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalisation of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimise the algorithm's performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimisation setting. To the best of our knowledge, these are the first regret bounds even for the Euclidean version of the problem. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.