Diagnosability is a system theoretical property characterizing whether fault occurrences in a system can always be detected within a finite time. In this paper, we investigate the verification of diagnosability for cyber-physical systems with continuous state sets. We develop an abstraction-free and automata-based framework to verify (the lack of) diagnosability, leveraging a notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hybrid barrier certificates</i>. To this end, we first construct a (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\delta,K$</tex-math></inline-formula>)-deterministic finite automaton that captures the occurrence of faults targeted for diagnosis. Then, the verification of diagnosability property is converted into a safety verification problem over a product system between the automaton and the augmented version of the dynamical system. We demonstrate that this verification problem can be addressed by computing hybrid barrier certificates for the product system. To this end, we introduce two systematic methods, leveraging sum-of-squares programming and counter-example guided inductive synthesis to search for such certificates. Additionally, if the system is found to be diagnosable, we propose methodologies to construct a diagnoser to identify fault occurrences online. Finally, we showcase the effectiveness of our methods through a case study.

In this paper, we establish a connection between the spectral theory of the Koopman operator and the solution of the Hamilton Jacobi (HJ) equation. The HJ equation occupies a central place in systems theory, and its solution is of interest in various control problems, including optimal control, robust control, and input-output analysis. A Hamiltonian dynamical system can be associated with the HJ equation and the solution of the HJ equation can be extracted from the Hamiltonian system in the form of Lagrangian submanifold. One of the main contributions of this paper is to show that the Lagrangian submanifolds can be obtained using the spectral analysis of the Koopman operator. We present two different procedures for the approximation of the HJ solution. We utilize the spectral properties of the Koopman operator associated with the uncontrolled dynamical system and Hamiltonian systems to approximate the HJ solution. We present a convex optimization-based computational framework with convergence analysis for approximating the Koopman eigenfunctions and the Lagrangian submanifolds. Our solution approach to the HJ equation using Koopman theory provides for a natural extension of results from linear systems to nonlinear systems. We demonstrate the application of this work for solving the optimal control problem. Finally, we present simulation results to validate the paper's main findings and compare the performance of the proposed controller against different controllers.

The resilient consensus problem is investigated in this paper for a class of networked Euler-Lagrange systems with event-triggered communication in the presence of Byzantine attacks. One challenge that we face in addressing the considered problem is the inapplicability of existing resilient decision algorithms designed for one-dimensional multi-agent systems. This is because the networked Euler-Lagrange systems fall into the category of multi-dimensional multi-agent systems with coupling among state vector components. To address this problem, we propose a new resilient decision algorithm. This algorithm constructs auxiliary variables related to the coordinative objectives for each normal agent, and transforms the considered resilient consensus problem into the consensus problem of the designed auxiliary variables. Furthermore, to relax the constraints imposed on Byzantine agent behavior patterns within continuous-time scenarios, the event-triggered communication scheme is adopted. Finally, the effectiveness of the proposed algorithm is demonstrated through case studies.

A novel and fully distributed optimization method is proposed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network under the uniformly jointly strongly connected (UJSC) assumption. Firstly, an approximated DRCP (ADRCP) is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints to ensure tractability and restricting the right-hand side of the constraints with a positive parameter to ensure a feasible solution for (DRCP) can be obtained. This problem is iteratively solved by a distributed projected gradient algorithm proposed in this paper, which is based on epigraphic reformulation and gradient projected operations. Secondly, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed local feasibility for each agent. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and adding the cutting-surfaces into the existing finite set of constraints. Thirdly, to ensure finite-time termination of the distributed optimization, a distributed termination algorithm is developed based on consensus and zeroth order stopping conditions under UJSC graphs. Fourthly, it is proved that the cutting-surface consensus approach terminates finitely and yields a feasible and approximate optimal solution for each agent. Finally, the effectiveness of the approach is illustrated through a numerical example

This paper introduces robust control barrier functions for uncertain parameter-varying control affine systems, where the parametric uncertainties can be time-varying and nonlinearly affecting the system dynamics and/or safety sets. In particular, we propose two methods based on mixed-monotone decomposition and concave bounding, where the controlled invariance condition remains linear in the control inputs despite nonlinear uncertainties. Moreover, we design alternative robust control Lyapunov functions where the control inputs also appear linearly; thus, these robust control barrier and Lyapunov functions can be coupled to obtain a quadratic program that can be solved online. Additionally, we propose two set-membership parameter estimation methods using polyhedral intersections and interval observers to reduce the conservatism of the robust approaches. Our robust approaches are observed to have comparable performance with adaptive approaches and robust safety guarantees, even when the (robust) adaptive methods may not.

This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the decision variables (e.g., a global cost gradient or constraint) and introduce a distributed consensus-oriented scheme to asymptotically approximate the unavailable information at each agent. Then, we delineate the proper methodology for intertwining the identified building blocks, i.e., the optimization-oriented method and the consensus-oriented one. The key intuition is to interpret the obtained interconnection as a singularly perturbed system. We rely on this interpretation to provide sufficient conditions for the building blocks to be successfully connected into a distributed scheme exhibiting the convergence guarantees of the centralized algorithm. Finally, we show the potential of our approach by developing a new distributed scheme for constraint-coupled problems with a linear convergence rate.

This work proposes a policy learning algorithm for seeking generalised feedback Nash equilibria (GFNE) in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{P}$</tex-math></inline-formula>-player noncooperative dynamic games. We consider linear-quadratic games with stochastic dynamics and design a best-response dynamics in which players update and broadcast a parametrisation of their state-feedback policies. Our approach leverages the System Level Synthesis (SLS) framework to formulate each player's update rule as the solution to a robust optimisation problem. Under certain conditions, rates of convergence to a feedback Nash equilibrium can be established. The algorithm is showcased in exemplary problems ranging from the decentralised control of unstable systems to competition in oligopolistic markets.

This paper addresses the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> output regulation problem of affine nonlinear systems with unmeasurable states and completely unknown dynamics. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> output regulation problem is formulated into a two-player zero-sum differential game problem with the control input and disturbance being the two adversary players. A model-based global state- feedback optimal solution to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> output regulation problem is presented by solving a Hamilton-Jacobi-Isaacs (HJI) equation, and a state- feedback reinforcement learning (RL) algorithm is proposed to solve the HJI equation without knowledge of system dynamics. A linear data-driven observer is designed to estimate the unmeasurable states and a novel output- feedback RL algorithm is developed based on the state- feedback RL framework by employing a critic-actor-disturbance neural network (NN) with a hidden layer. The salient found of this work is that, under the proposed output- feedback RL algorithm, the closed-loop system can reach globally stable. A numerical example is provided to demonstrate the effectiveness of the proposed solution.

Structural identifiability concerns the question of which unknown parameters of a model can be recovered from (perfect) input-output data. If all of the parameters of a model can be recovered from data, the model is said to be identifiable. However, in many models, there are parameters that can take on an infinite number of values but yield the same input-output data. In this case, those parameters and the model are called unidentifiable. The question is then what to do with an unidentifiable model. One can try to add more input-output data or decrease the number of unknown parameters, if experimentally feasible, or try to find a reparametrization to make the model identifiable. In this paper, we take the latter approach. While existing approaches to find identifiable reparametrizations were limited to scaling reparametrizations or were not guaranteed to find a globally identifiable reparametrization even if it exists, we significantly broaden the class of models for which we can find a globally identifiable model with the same input-output behavior as the original one. We also prove that, for linear models, a globally identifiable reparametrization always exists and show that, for a certain class of linear compartmental models, with and without inputs, an explicit reparametrization formula exists. We illustrate our method on several examples and provide detailed analysis in supplementary material on github.