Class Of Nonlinear Hybrid Systems Research Articles

SAT-Reach : A Bounded Model Checker for Affine Hybrid Systems

Bounded model checking (BMC) is well-known to be undecidable even for simple hybrid systems. Existing work targeted for a wide class of non-linear hybrid systems reduces the BMC problem to the satisfiability problem of an satisfiability modulo theory formula encoding the hybrid system dynamics. Consequently, the satisfiability of the formula is deduced with a δ-decision procedure. However, the encoded formula can be complex for large automaton and for deep exploration causing the decision procedure to be inefficient. Additionally, a generalized decision procedure can be inefficient for hybrid systems with simple dynamics. In this article, we propose a BMC algorithm built upon the foundation of the counter example guided abstraction refinement (CEGAR) technique and targeted for hybrid systems with piecewise affine dynamics, modeled as a hybrid automaton. In particular, our algorithm begins by searching an abstract counterexample in the discrete state-space of the automaton. We check whether a discovered abstract counterexample is spurious or real by a two-tier refinement of the state-space guided by the abstract counterexample. The primary refinement is through symbolic reachability analysis and the following refinement is via a search of a real counterexample by the trajectory splicing method, guided in turn by the outcome of reachability analysis. We show that our algorithm reaps the benefits of the CEGAR technique by directing the exploration in the regions of interest and pruning search space that is irrelevant to the property under consideration. In addition, an optimization by memoizing the computed symbolic states during reachability analysis has been proposed for efficiency. The proposed algorithm is implemented in the tool SAT-Reach, and we compare its performance with dReach , XSpeed , Flow* , SpaceEx, and a pattern database heuristic-guided search algorithm. Experiments demonstrate the efficacy of our algorithm.

Optimal Control of Nonlinear Hybrid Systems Driven by Signed Measures with Variable Intensities and Supports

In this paper we consider a class of nonlinear hybrid systems controlled by discrete signed measures. We develop a new technique to determine the optimal sizes and the optimal time instants for app...

Hybrid output regulation for nonlinear systems: Steady-state vs receding horizon formulation

The hybrid output regulation problem in the presence of periodic jumps is approached in this paper for a class of nonlinear hybrid systems satisfying rather mild assumptions. We provide sufficient conditions that characterize steady-state trajectories achieving output regulation that are defined, mimicking the linear case, in terms of two equations: the first one describes the solution of a flow-only output regulation problem, while the second is associated to an auxiliary output regulation problem concerning the monodromy equivalent system of the flow zero-dynamics. Such conditions are then revisited and a receding-horizon, steady-state-less, solution to the (hybrid) output regulation problem is suggested, based on the solution of a sequence of two-point boundary value problems.

Frequency-domain estimates of the sampling interval in multirate nonlinear systems by time-delay approach

ABSTRACTA class of nonlinear hybrid systems consisting of a continuous plant and a multirate sampled-data controller is considered. Applying the time-delay approach, the system is transformed to the system with a time-varying sawtooth delay. Then, the value of the sampling intervals ensuring stability of the closed-loop system is estimated based on the frequency-domain circle-like criterion for systems with time-varying delay. Such a criterion for multirate MIMO systems is established based on the previous result for SISO systems proposed by M.Churilova in 1995. Efficiency and advantages of the method are illustrated by numerical examples. The key advantage of the proposed approach is that it is applicable to multirate systems nonaffine in control. It allows one to use a nonlinear feedback for stabilisation. Particularly, the case of nonsmooth or discontinuous nonlinear systems can be treated.

Input–output finite-time stabilization of a class of nonlinear hybrid systems based on FSM with MDADT

This thesis investigates the problem of input–output finite-time stabilization for a class of nonlinear impulsive hybrid systems based on finite state machine (FSM). First, the concept of input–output finite-time stability (IO-FTS) is extended for such hybrid systems, then, the stability analysis is given by combining the multiple Lyapunov functions (MLFs) method and mode-dependent average dwell time (MDADT) technique, the corresponding sufficient conditions are derived and proved. Furthermore, a state feedback controller is designed to stabilize the hybrid systems. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed controller.

Global stability analysis of switched nonlinear observers

This paper considers the problem of simultaneous estimation of the system states and the strategy of commutation for a larger class of nonlinear switched systems. First, a hybrid high gain observer is considered to get the exact estimation of the continuous states where the strategy of switching is previously known. Then, an extension to a larger class of nonlinear hybrid systems with arbitrary switching is made. Stability analysis is widely discussed for the two cases to provide a finite-time convergence of the estimation errors. The effectiveness of the proposed hybrid high gain observer has been proved by applying it to a quadruple tank process.

Fault detection and identification of non‐linear hybrid system using self‐switched sigma point filter bank

This study proposes a scheme for fault detection and identification (FDI) of a class of non-linear hybrid systems. For fault detection, the proposed method uses a self-switched unscented Kalman filter (UKF) where a component filter with the appropriate dynamic model is chosen to suit the current mode of the hybrid plant. The mode of the hybrid plant, usually defined by system states, is deduced based on the state estimates. The statistical tests of measured datasets are used to detect and identify the fault parameters. For fault identification, a bank of such switched UKF filters is used. A three-tank system has been used to demonstrate the effectiveness of the scheme. Different types of faults, that is, leakage, clogging and abrupt changes in inflow (actuator fault) have been considered. t-Statistical test has been performed on the residuals for FDI and threshold calculation purposes. It is shown that all the types of faults can be successfully detected and identified by the proposed method. The performance of the proposed system is compared with the same for an extended Kalman filter-based FDI system. It has been shown that the UKF-based scheme has lower latency and higher range coverage.

Transverse Dynamics and Regions of Stability for Nonlinear Hybrid Limit Cycles

AbstractThis paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from the linearization of the transverse dynamics construct a quadratic candidate Lyapunov function; (3) search for a new Lyapunov function verifying maximal regions of orbital stability via iterated of sum-of-squares programs. The construction of the transverse dynamics is novel, and valid for a broad class of nonlinear hybrid systems.

Stationary oscillation of an impulsive delayed system and its application to chaotic neural networks

This paper investigates the stationary oscillation for an impulsive delayed system which represents a class of nonlinear hybrid systems. First, a new concept of S-stability is introduced for nonlinear impulsive delayed systems. Based on this new concept and fixed point theorem, the relationship between S-stability and stationary oscillation (i.e., existence, uniqueness and global stability of periodic solutions) for the nonlinear impulsive delayed system is explored. It is shown that the nonlinear impulsive delayed system has a stationary oscillation if the system is S-stable. Second, an easily verifiable sufficient condition is then obtained for stationary oscillations of nonautonomous neural networks with both time delays and impulses by using the new criterion. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.

On the stability of a class of nonlinear hybrid systems

In this paper, we propose new conditions for guaranteeing the stability of nonlinear sampled data systems. In order to do this, we extend Lyapunov theory to this class of systems.

On the stability of a class of nonlinear hybrid systems

In this paper, we propose new conditions to guarantee the stability of nonlinear sampled data systems. In order to do this, we extend lyapunov theory to this class of systems.