ABSTRACT. Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous evolution of a hybrid system such that the evolution depends not only on the present state but also on its execution history, or in the discrete switching between its different control modes. In this paper we come up with a new model of hybrid systems, called \emph{delay hybrid automata}, to capture the dynamics of systems with the aforementioned two kinds of delays. Furthermore, based upon this model we study the robust switching controller synthesis problem such that the controlled delay system is able to satisfy the specified safety properties regardless of perturbations. To the end, a novel method is proposed to synthesize switching controllers based on the computation of differential invariants for continuous evolution and backward reachable sets of discrete jumps with delays. Finally, we implement a prototypical tool of our approach and demonstrate it on some case studies.

ABSTRACT. Hybrid systems are widely used in safety-critical areas. Hybrid optimal control synthesis, which aims to generate an optimal sequence of control inputs for a given task, is one of the most important problems in the field. The existing hybrid optimal control algorithms mainly include gradient-based and sampling-based methods. Gradient-based methods are efficient but they require the system under control should be differentiable. Sampling-based methods have no such limitations, but the ability of existing ones to solve complex control missions is restricted.

In this paper, we concern about a general class of hybrid systems without any limitations and propose a practical and efficient method to solve complex hybrid optimal control problems. Basically, we transform the control synthesis problem of each control sequence in a hybrid system into a derivative-free optimization (DFO) problem. Then, by adapting a start-of-art classification-based DFO method, we design a specific DFO algorithm based on sampling to solve such problems efficiently. Furthermore, for complex state space, which is difficult to solve, we present a piecewise control synthesis method to make a tradeoff between optimality and efficiency by generating feasible and piecewise optimal control inputs instead. The empirical results on two complex real-world hybrid systems: a vehicle and a quadcopter drone system, demonstrate that our method outperforms existing methods significantly.

ABSTRACT. Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach.

ABSTRACT. This paper presents path-dependent feedback controllers and estimators with bounded tracking and estimation error guarantees for discrete-time affine systems with time-varying delayed and missing data, where the set of all temporal patterns for the missing or delayed data is constrained by a fixed-length language. In particular, we propose two controller/estimator synthesis approaches based on output feedback and output error feedback parameterizations such that the tracking or estimation errors satisfy a property known as equalized recovery, where the errors are guaranteed to satisfy a recovery level at the start and the end of a finite time horizon, but may temporarily increase (by a bounded amount) within the horizon. To achieve this, we introduce a mapping of the fixed-length delayed/missing data language onto a reduced event-based language, and present designs with feedback gain matrices that adapt based on the observed path in the reduced language, resulting in improved performance. Furthermore, we propose a word observer that finds the set of words (i.e., the delayed/missing data patterns) in the original fixed-length language that are compatible with the observed path. The effectiveness of the proposed approaches when compared to existing approaches is demonstrated using several illustrative examples.

ABSTRACT. In this paper, we present a quantization scheme that reconstructs the state of linear switched systems with a prescribed exponential decaying rate for the state estimation error. We show how to use the Lyapunov exponents and a geometric object called Oseledets' filtration to design such a quantization scheme. Then, we prove that this algorithm works at an average data-rate close to the estimation entropy of the given system. Furthermore, we can choose the average data-rate to be arbitrarily close to the estimation entropy whenever the linear switched system has the so-called regularity property. We show that, under the regularity assumption, the quantization scheme is completely causal in the sense that it only depends on information that is available at the current time instant. Finally, we present simulation results for a Markov Jump Linear System, a class of systems for which the realizations are known to be regular with probability $1$.

ABSTRACT. In the context of networked control systems, event-triggered control (ETC) has emerged as a major topic due to its alleged resource usage reduction capabilities. However, this is mainly supported by numerical simulations, and very little is formally known about the traffic generated by ETC. This work devises a method to estimate, and often to determine exactly, the minimum average inter-sample time (MAIST) generated by periodic event-triggered control (PETC) of linear systems. The method involves abstracting the traffic model using a bisimulation refinement algorithm and finding the cycle of minimum average length in the graph associated to it. This always gives a lower bound to the actual MAIST. Moreover, if this cycle turns out to be related to a periodic solution of the closed-loop PETC system, the performance metric is exact.