Model simplification for switched hybrid systems

This paper is concerned with the problem of model reduction for switched system, which is an important class of hybrid systems frequently encountered in practical situations. Two sharply different approaches are proposed to solve this problem. The first approach casts the model reduction into a convex optimization problem, which is the first attempt to solve the model reduction problem by using linearization procedure. The second one, based on the cone complementarity linearization idea, casts the model reduction problem into a sequential minimization problem subject to linear matrix inequality constraints. Both approaches have their own advantages and disadvantages concerning conservatism and computational complexity. A numerical example illustrates the effectiveness of the proposed theories.     

Continuous selections of trajectories of hybrid systems

We present results on existence of continuous selections of trajectories of hybrid systems evolving according to Lipschitz nonlinear inclusions. First, we utilize the Skorohod metric to define both a family of pseudo-metrics and a metric on the set of trajectories accepted by the hybrid automaton. We show that under a non-Zeno condition the latter metric is complete. Second, the existence of continuous selections with respect to the family of pseudo-metrics is proved under a relatively mild assumption of transversality.     

一类混杂系统的生存控制设计

研究了混杂系统关于由不等式表示的区域的生存控制设计问题.首先基于非光滑分析理论给出了系统关于所给区域生存的一个充分条件;然后给出相应的生存控制设计方法.该方法将系统的生存控制输入的选择问题转化为求解非光滑优化问题和二次规划问题.     

Control for discrete singular hybrid systems

The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach.     

Reachability analysis of complex planar hybrid systems

Hybrid systems are systems that exhibit both discrete and continuous behavior. Reachability, the question of whether a system in one state can reach some other state, is undecidable for hybrid systems in general. In this paper we are concerned with GSPDIs, 2-dimensional systems generalizing SPDIs (planar hybrid systems based on “simple polygonal differential inclusions”), for which reachability have been shown to be decidable. GSPDIs are useful to approximate 2-dimensional control systems, allowing the verification of safety properties of such systems.     

Abstractions for hybrid systems

We present a procedure for constructing sound finite-state discrete abstractions of hybrid systems. This procedure uses ideas from predicate abstraction to abstract the discrete dynamics and qualitative reasoning to abstract the continuous dynamics of the hybrid system. It relies on the ability to decide satisfiability of quantifier-free formulas in some theory rich enough to encode the hybrid system. We characterize the sets of predicates that can be used to create high quality abstractions and we present new approaches to discover such useful sets of predicates. Under certain assumptions, the abstraction procedure can be applied compositionally to abstract a hybrid system described as a composition of two hybrid automata. We show that the constructed abstractions are always sound, but are relatively complete only under certain assumptions.     

Output-to-state stability for hybrid systems

Output-to-state stability (OSS) is a dual notion of input-to-state stability for dynamical systems. This paper presents Lyapunov and asymptotic characterizations of OSS for hybrid dynamical systems, emphasizing that a globally detectable (i.e. nonuniformly OSS) hybrid system admits a smooth OSS-Lyapunov function.     

Algorithmic analysis of polygonal hybrid systems,Part II: Phase portrait and tools

Polygonal differential inclusion systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. The reachability problem as well as the computation of certain objects of the phase portrait is decidable. In this paper we show how to compute the viability, controllability and invariance kernels, as well as semi-separatrix curves for SPDIs. We also present the tool SPeeDI⁺, which implements a reachability algorithm and computes phase portraits of SPDIs.     

Kalman filter for controlled hybrid systems

The linear partially observed discrete-continuous (hybrid) stochastic controllable system described by differential equations with measures is considered. The optimal filtering equations in the form of generalized Kalman filter are obtained in the case of non-anticipating control. This result could be a theoretical basis for the optimal control in stochastic hybrid systems with incomplete information.     

混杂系统的预测控制

因混杂系统预测控制（PC-HS）具有在线处理控制量和状态量的约束等优点,而成为学术界研究的一个热点．系统地论述了PC-HS的发展和研究现状,在介绍混杂系统的背景和模型的基础上,重点讨论了PC-HS的各种算法、性能等几个前沿问题,并对PC-HS目前研究中存在的问题进行了分析,对未来的一些研究方向进行了展望．     

Wirtinger-based integral inequality: Application to time-delay systems

In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is a relevant issue and always an open problem. In this paper, we propose an alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities. It is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions. In order to illustrate the potential gain of employing this new inequality with respect to the Jensen one, two applications on time-delay and sampled-data stability analysis are provided.     

Safety verification and reachability analysis for hybrid systems

Safety verification and reachability analysis for hybrid systems is a very active research domain. Many approaches that seem quite different, have been proposed to solve this complex problem. This paper presents an overview of various approaches for autonomous, continuous-time hybrid systems and presents them with respect to basic problems related to verification.     

A hybrid receding-horizon control scheme for nonlinear systems

A hybrid receding-horizon control scheme for nonlinear discrete-time systems is proposed. Whereas a set of optimal feedback control functions is defined at the continuous level, a discrete-event controller chooses the best control action, depending on the current conditions of a plant and on possible external events. Such a two-level scheme is embedded in the structure of abstract hybrid systems, thus making it possible to prove a new asymptotic stability result for the hybrid receding-horizon control approach.     

Regularizability of complex switched server queueing networks modelled as hybrid dynamical systems

The paper considers the problem of the qualitative analysis of complex switched server queueing networks. Such networks can be used to model various flexible manufacturing, communications, and computer systems. We introduce the concept of regularizability for such systems and obtain a necessary and sufficient condition for a switched server queueing network to be regularizable.     

Energy-based control for hybrid port-controlled Hamiltonian systems

In this paper we develop an energy-based hybrid control framework for hybrid port-controlled Hamiltonian systems. In particular, we obtain constructive sufficient conditions for hybrid feedback stabilization that provide a shaped energy function for the closed-loop system, while preserving a hybrid Hamiltonian structure at the closed-loop level. Furthermore, an inverse optimal hybrid feedback control framework is developed that characterizes a class of globally stabilizing energy-based controllers that guarantee hybrid sector and gain margins to multiplicative input uncertainty of hybrid Hamiltonian systems.     

A computational approach to synthesizing guards for hybrid systems

We propose a technique for synthesizing switching guards for hybrid systems to satisfy a given state-based safety constraint. Using techniques from sum of squares (SOS) optimization, we design guards defined by semialgebraic sets that trigger mode switches, and we guarantee that the synthesized switching policy does not allow Zeno executions. We demonstrate our approach on an example of switched affine systems and on an application to traffic ramp metering.     

A hybrid splitting method for variational inequality problems with separable structure

Alternating direction method (ADM), which decomposes a large-scale original variational inequality (VI) problem into a series of smaller scale subproblems, is very attractive for solving a class of VI problems with a separable structure. This type of method can greatly improve the efficiency, but cannot avoid solving VI subproblems. In this paper, we propose a hybrid splitting method with variable parameters for separable VI problems. Specifically, the proposed method solves only one strongly monotone VI subproblem and a well-posed system of nonlinear equations in each iteration. The global convergence of the new method is established under some standard assumptions as those in classical ADMs. Finally, some preliminary numerical results show that the proposed method performs favourably in practice.     

Representations and structural properties of periodic systems

We consider periodic behavioral systems as introduced in [Kuijper, M., & Willems, J. C. (1997). A behavioral framework for periodically time-varying systems. In Proceedings of the 36th conference on decision & control (Vol. 3, pp. 2013-2016). San Diego, California, USA, 10-12 December 1997] and analyze two main issues: behavioral representation/controllability and autonomy. More concretely, we study the equivalence and the minimality of kernel representations, and introduce latent variable (and, in particular, image) representations. Moreover we relate the controllability of a periodic system with the controllability of an associated time-invariant system known as lifted system, and derive a controllability test. Further, we prove the existence of an autonomous/controllable decomposition similar to the time-invariant case. Finally, we introduce a new concept of free variables and inputs, which can be regarded as a generalization of the one adopted for time-invariant systems, but appears to be more adequate for the periodic case.     

Dynamical properties of hybrid systems simulators

This paper analyzes the dynamical properties of a class of hybrid systems simulators. A hybrid system is a dynamical system with a state that can both flow and jump. Its simulator attempts to generate its solutions approximately. The paper presents mild regularity conditions on the hybrid system and its simulator to guarantee that simulated solutions are close to actual solutions on compact (hybrid) time intervals, and that asymptotically stable compact sets are preserved, in a semiglobal practical sense, under simulation. In fact, it is established that asymptotically stable compact sets are continuous in the integration step size parameter of the simulator; that is, as the step size of the simulator converges to zero, the asymptotically stable set observed in simulations approaches the asymptotically stable compact set of the true hybrid system. Examples are used to illustrate concepts and results.