Analysis and control of hybrid systems with parameter uncertainty based on interval methods

A survey of modeling and control of hybrid systems

This paper proposes an approach for the analysis and control of hybrid systems based on the hybrid automaton model. The problem that must be solved can be formulated as follows: given a hybrid automaton how can be restricted the regions associated with the controllable transition, in a systematic way, so that all the remaining behaviors satisfy certain properties. The hybrid nature of the manufacturing system is also investigated as a case study represented by a manufacturing cell. Throughout this paper the proposed methods are illustrated using an example taken from the manufacturing domain.

Welcome to the proceedings of the 23rd ACM International Conference on Hybrid Systems: Computation and Control (HSCC 2020), held virtually for the first time. HSCC focuses on original research that involves concepts, tools, and techniques from computer science, control theory, and applied mathematics for the analysis and control of hybrid systems with an emphasis on computational aspects. Papers in HSCC range over a wide spectrum of topics from theoretical results to practical considerations, and from academic research to industrial adoption. Techniques presented at HSCC are applicable to both man-made cyber-physical systems and physical systems that naturally exhibit hybrid behavior.

Data-driven hybrid switched-gain estimation for hybrid systems with periodic jumps.

Hybrid system analysis and control via mixed integer optimization

The traditional isolation approach can suppress the seismic responses of upper structure and at the same time induce substantial deformation of isolation layer. Excessive base drift may cause the degradation and even the damage of the isolation system. Therefore, supplemental control devices can be implemented in the common base isolation system to construct hybrid control system and reduce the base drifts of structures. The seismic mitigation of a building frame with hybrid control system is carried out in this study. The mechanical model of magnetorheological (MR) damper is presented by involving the effects of brace stiffness of the damper. The equation of motion of a frame structure with stiffness eccentricity incorporated with intelligent hybrid control system disturbed by seismic excitations is established by considering the effects of both isolators and MR dampers. A clipped-optimal strategy based on fuzzy control principle is proposed for MR dampers. A building frame is taken as the example to examine the feasibility and reliability of the proposed intelligent control approach. The efficacy of the hybrid control approach is compared with the base isolation approach. An extensive parametric study is carried out to find the optimal parameters of MR dampers, by which the maximum reduction of seismic responses may be achieved, and to assess the effects of earthquake intensity and brace stiffness on damper performance. The work on example buildings showed that the installation of the smart dampers with proper parameters and proper control strategy could significantly reduce seismic responses of structures, and the performance of the smart damper is better than that of the common base isolation system. The optimal parameters of the MR dampers could be identified through a parametric study.

We propose a procedure for synthesizing piecewise linear optimal controllers for discrete-time hybrid systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted l/sub 1///spl infin/-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a multiparametric mixed-integer linear program, which avoids solving mixed-integer programs online. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation.

Hybrid Control Systems are increasingly investigated as models for control systems where the interaction between continuous and discrete processes is tightly integrated. As yet, there is no general agreement as to what constitutes a canonical hybrid system. Rather various subclasses of systems combining continuous evolution and discrete event characteristics are analyzed for each application. In this dissertation we first unify the presentation of hybrid systems with a rich model which encompasses most examples of interest. We classify the available results and show how they fit together within the different subcategories. In the main part of the dissertation we prove that for piecewise linear control systems---introduced over twenty years ago---the isomorphism problem is decidable in polynomial time in the number of inequalities defining the sets and the dimension of the sets. We also prove a stability result for switching systems arising from the problem of vehicle formations.

The synergy between optimization and control is a long standing tradition. In fact, this synergy is becoming more and more apparent because of the multi-disciplinary character of the most pressing, current engineering problems along with constant developments of these two fields. Historically, optimization methods have helped the control community to achieve their design goals formalized in some sort of objective function. On the other hand, control theory has provided a setting to interpret complicated aspects of optimization algorithms. In this thesis, we address three problem instances that lie on the boundary of optimization and control. We employ tools from one field to address a problem in the other field. Fundamentally, our proposed methods share a similar character: their analysis techniques are trajectory-based. In simple words, our proposed methods exploit the trajectories generated by the dynamics that represent each problem instance. The first problem focuses on a 2nd-order, damped differential equation (ODE). This ODE along with its numerous variations have been used to develop or analyze various optimization algorithms, known as fast methods. As an alternative to the existing methods, we first amend the underling ODE with two types of state-dependent inputs, and then extend the resulting controlled dynamics to two hybrid control systems. Employing a trajectory-based analysis, both control laws are constructed to guarantee exponential convergence in a suboptimality measure. To show that the trajectories generated by each hybrid control system are well-posed, we demonstrate Zeno-freeness of solution trajectories in both cases. Furthermore, we propose a mechanism to determine a time-discretization step-size such that the resulting discrete-time hybrid control systems are exponentially stable. Event-based implementation of control laws have received a lot of attention during the past decade. The reason for this interest is the hope to reduce the conservatism involved in the traditional periodic implementation. In the second problem of this thesis, we introduce an event-based sampling policy for a constraint-tightening, robust model predictive control (RMPC) method. The triggering mechanism is a sequence of hyper-rectangles constructed around the optimal state trajectories. In particular, the triggering mechanism's nature makes the proposed approach a suitable choice for plants without a centralized sensory node. A key feature of the proposed method is its complete decoupling from the RMPC method's parameters, facilitating a meaningful comparison between the periodic and aperiodic implementation policies. Furthermore, we provide two types of convex formulations to design the triggering mechanism. The last problem we focus on in this thesis is also related to the event-based implementation of a control law. However, the main aim here is to propose an entity that can be utilized by a real-time engineer to schedule tasks in a networked structure. A common entity provided in the literature related to event-triggering approaches is the minimal inter-execution time (to show the avoidance of a Zeno behavior in the closed-loop system). Nonetheless, such a quantity is extremely conservative when used for scheduling purposes. In this problem, we consider an $\mathcal{L}_2$-based triggering mechanism introduced in the literature and propose a framework to construct a timed safety automaton that can capture the triggering instants generated by this mechanism. In our analysis, we borrow some tools from stability analysis of delayed systems along with reachability analysis to construct the desired timed safety automaton.

The high cost of international economic and financial crises highlights the need for a comprehensive framework to assess the robustness of national economic and financial systems. This paper proposes a new comprehensive approach to measure, analyze, and manage macroeconomic risk based on the theory and practice of modern contingent claims analysis (CCA). We illustrate how to use the CCA approach to model and measure sectoral and national risk exposures, and analyze policies to offset their potentially harmful effects. This new framework provides economic balance sheets for inter-linked sectors and a risk accounting framework for an economy. CCA provides a natural framework for analysis of mismatches between an entity's assets and liabilities, such as currency and maturity mismatches on balance sheets. Policies or actions that reduce these mismatches will help reduce risk and vulnerability. It also provides a new framework for sovereign capital structure analysis. It is useful for assessing vulnerability, policy analysis, risk management, investment analysis, and design of risk control strategies. Both public and private sector participants can benefit from pursuing ways to facilitate more efficient macro risk accounting, improve price and volatility discovery, and expand international risk intermediation activities.

A Unified Approach for Controllability Analysis of Hybrid Control Systems

Constraint-based analysis of concurrent probabilistic hybrid systems: An application to networked automation systems

Modelling and analysis of hybrid systems

This thesis focuses on Model Predictive Control (MPC) of discrete-time hybrid systems. Hybrid systems contain continuous and discrete valued components, and are located at the intersection between the fields of control theory and computer science. MPC uses an internal model of the controlled plant to predict the future evolution of the controlled variables over a prediction horizon. A cost function is minimized to obtain the optimal control input sequence, which is applied to the plant by means of a receding horizon policy. The latter implies that only the first control input of the input sequence is implemented, the horizon is shifted by one time-step and the above procedure is repeated at the next sampling instant. Most importantly, theory and tools are available to off-line derive the piecewise affine (PWA) state-feedback control law. Hence, any time-consuming on-line computation of the control input is avoided and plants with high sampling frequencies can be controlled. The thesis is divided into two parts: The first part is devoted to theory and algorithms, whereas the second part tackles applications in the fields of power electronics and power systems. In the first part, using the notion of cell enumeration in hyperplane arrangements from computational geometry, we propose an algorithm that efficiently enumerates all feasible modes of a composition of hybrid systems. This technique allows the designer to evaluate the complexity of the compound model, to efficiently translate the model into a PWA representation, and to reduce the computational burden of optimal control schemes by adding cuts that prune infeasible modes from the model. With respect to implementation, an important issue is the complexity reduction of PWA state-feedback controllers. Hence, we propose two algorithms that solve the problem of deriving a PWA representation that is both equivalent to the given one and minimal in the number of regions. As both algorithms refrain from solving additional Linear Programs, they are not only optimal but also computationally feasible. In many cases, the optimal complexity reduction constitutes an enabling technique when implementing the optimal controllers as look-up tables in hardware. In the second part of the thesis, we consider the field of power electronics that is intrinsically hybrid, since the positions of semiconductor switches are described by binary variables. The fact that the methodologies of MPC and hybrid systems are basically unknown in the power electronics community has motivated us to consider such problems, namely

This paper collects work on the analysis of hybrid systems. The hybrid systems considered are those that combine continuous dynamics (represented by differential or difference equations) with finite dynamics, usually thought of as being a finite automaton. We review multiple Lyapunov functions as a tool for analyzing Lyapunov of general hybrid systems. Background results, the author's introductory work, and subsequent extensions are covered. Specializing to hybrid systems with linear dynamics in each constituent mode and linear jump operators, we review some key theorems of Barabanov-Staroshilov (1988), and give corollaries encompassing several recently-derived stability by first approximation theorems in the literature. We also comment on the use of computational tests for of hybrid systems, and the general complexity. The result is a tutorial on the state of the art in theory and computation of hybrid systems stability.