模式转换未知的一类混杂系统的状态估计

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.     

State Estimation of a Class of Hybrid Systems in the Presence of Unknown Mode Transitions

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics,the state estimation of hybrid systems becomes a challenging problem.It is more com- plicated when the discrete mode transition information is not available,and the modes of hybrid systems are nonlinear stochastic dynamic systems.To address this problem,this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochas- tic systems with unknown mode transition,the method for designing HSTF is presented.The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition in- formation,and the estimation of hybrid states is robust against the initial state.Simulation results illustrate the effectiveness of the proposed approach.     

线性混合系统的可观性分析

线性混合系统的控制输入(包括离散控制和连续控制)会影响混合系统的状态可观性．混合系统的可观性包括初始的离散状态和连续状态，以及离散状态的切换时间．对此．分析了系统的控制输入对线性混合系统状态(主要是离散状态)的影响，并论述这将有助于改善某些线性混合系统状态的可观性．通过分析给出了在这种情形下比较宽松的线性混合系统状态可观性条件及其秩检验条件，并给出说明性示例．     

Computational techniques for hybrid system verification

This paper concerns computational methods for verifying properties of polyhedral invariant hybrid automata (PIHA), which are hybrid automata with discrete transitions governed by polyhedral guards. To verify properties of the state trajectories for PIHA, the planar switching surfaces are partitioned to define a finite set of discrete states in an approximate quotient transition system (AQTS). State transitions in the AQTS are determined by the reachable states, or flow pipes, emitting from the switching surfaces according to the continuous dynamics. This paper presents a method for computing polyhedral approximations to flow pipes. It is shown that the flow-pipe approximation error can be made arbitrarily small for general nonlinear dynamics and that the computations can be made more efficient for affine systems. The paper also describes CheckMate, a MATLAB-based tool for modeling, simulating and verifying properties of hybrid systems based on the computational methods previously described.     

基于混合随机Petri网的一类混合系统的模型及稳定性

混合动态系统是包含离散事件系统（ＤＥＳ）和连续变量系统（ＣＶＳ）的复杂系统。讨论了一类每个离散状态包含一个连续动态系统,且离散事件具有Ｍａｒｋｏｖ链性质的随机混合系统,在提出利用混合随机Ｐｅｔｒｉ网的建模方法的基础上,给出混合均方稳定的概念、稳定性和可镇定条件,最后以一个简单的例子做子说明和仿真。     

Design of linear observers for a class of linear hybrid systems

This paper deals with the design of linear observers for a class of linear hybrid systems. Such systems are composed of continuous-time and digital substates and possess, in general, coupling dynamics between both substates. Two observer prototypes based on the prediction error are proposed. The first is based on the observation of an extended discrete system at sampling instants. The discrete extended state is composed of the sampled values of the continuous substate at sampling instants and the digital substate. The estimation of the continuous substate in between sampling instants is made by using the plant parametrization and the sampled prediction error at the preceding sampling instant. The continuous-time state estimates are reinitialized at each new sampling instant by taking values from the corresponding components of the discretized substate of the observer of the auxiliary discrete extended system. The second observer prototype estimates the continuous-time substate for all time from initial conditions which are taken only when the estimation algorithm starts. The observer involves feedback information of the current observation error, that of the preceding sampling instant and that associated with the estimation of the discrete system. As a result, the discontinuities of the estimated substate at sampling instants, which typically occur with the use of the first prototype, are not present in this observation scheme. The exponential convergence to zero of both prediction and observation errors may be ensured under observability and detectability assumptions Furthermore, prescribed pole placement of the state estimation error is achieved under observability of the discrete extended plant. Also, prescribed pole placement of the combined dynamics of the extended plant and observation error can be obtained. For that purpose, the extended hybrid plant is assumed to be controllable when the linear control input is generated from measurements of the state observation. in both observation prototypes.     

Analysis of Hybrid Systems Based on Hybrid Net Condition/Event System Model

In thispaper, hybrid net condition /event systems are introducedas a model for hybrid systems. The model consists of a discretetimed Petri net and a continuous Petri net which interact eachother through condition and event signals. By introducing timeddiscrete places in the model, timing constraints in hybrid systemscan be easily described. For a class of hybrid systems that canbe described as linear hybrid net condition /eventsystems whose continuous part is a constant continuous Petrinet, two methods are developed for their state reachability analysis.One is the predicate-transformation method, which is an extensionof a state reachability analysis method for linear hybrid automata.The other is the path-based method, which enumerates all possiblefiring seqenences of discrete transitions and verifies if a givenset of states can be reached from another set by firing a sequenceof discrete transitions. The verification is performed by solvinga constraint satisfaction problem. A technique that adds additionalconstraints to the problem when a discrete state is revisitedalong the sequence is developed and used to prevent the methodfrom infinite enumeration. These methods provide a basis foralgorithmic analysis of this class of hybrid systems.     

Partially‐observable stochastic hybrid systems (poshss) state estimation and optimal control

This paper discusses the state estimation and optimal control problem of a class of partially‐observable stochastic hybrid systems (POSHS). The POSHS has interacting continuous and discrete dynamics with uncertainties. The continuous dynamics are given by a Markov‐jump linear system and the discrete dynamics are defined by a Markov chain whose transition probabilities are dependent on the continuous state via guard conditions. The only information available to the controller are noisy measurements of the continuous state. To solve the optimal control problem, a separable control scheme is applied: the controller estimates the continuous and discrete states of the POSHS using noisy measurements and computes the optimal control input from the state estimates. Since computing both optimal state estimates and optimal control inputs are intractable, this paper proposes computationally efficient algorithms to solve this problem numerically. The proposed hybrid estimation algorithm is able to handle state‐dependent Markov transitions and compute Gaussian‐ mixture distributions as the state estimates. With the computed state estimates, a reinforcement learning algorithm defined on a function space is proposed. This approach is based on Monte Carlo sampling and integration on a function space containing all the probability distributions of the hybrid state estimates. Finally, the proposed algorithm is tested via numerical simulations.     

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.     

基于粒子滤波算法的混合系统监测与诊断

利用粒子滤波算法具有同时估计连续状态和离散状态的特点,提出一种可用于混合系统状态监测与诊断的新方法.给出了该方法的理论推导和设计步骤,讨论了在诊断应用中粒子滤波器所遇到的问题,并给出了改善的措施.仿真结果证明用粒子滤波器对混合系统进行监测与诊断是可行的,所提的方法对估计结果有比较好的改善.     

Controlling a Class of Nonlinear Systems on Rectangles

In this paper, we focus on a particular class of nonlinear affine control systems of the form xdot=f(x)+Bu, where the drift f is a multi-affine vector field (i.e., affine in each state component), the control distribution B is constant, and the control u is constrained to a convex set. For such a system, we first derive necessary and sufficient conditions for the existence of a multiaffine feedback control law keeping the system in a rectangular invariant. We then derive sufficient conditions for driving all initial states in a rectangle through a desired facet in finite time. If the control constraints are polyhedral, we show that all these conditions translate to checking the feasibility of systems of linear inequalities to be satisfied by the control at the vertices of the state rectangle. This work is motivated by the need to construct discrete abstractions for continuous and hybrid systems, in which analysis and control tasks specified in terms of reachability of sets of states can be reduced to searches on finite graphs. We show the application of our results to the problem of controlling the angular velocity of an aircraft with gas jet actuators     

混合系统二维离散与连续状态同步估计研究

在混合系统中,需要同时估计出系统的离散状态与连续状态.针对混合系统出现二维离散状态下的混合状态估计问题进行研究,根据系统特性,采用跳变马尔可夫线性系统建模,并应用Rao-Blackwellised粒子滤波算法对二维离散状态与连续状态进行同步估计.由于算法一定程度上缓解了粒子滤波算法在高维状态空间估计中的失效问题,并对离散状态单独采样,能提高系统状态的估计精度.仿真试验证明,方法能有效地同步估计出系统的二维离散状态与连续状态,其中,二维离散状态的估计准确率达到了96%.     

A continuous optimization framework for hybrid system identification

We propose a new framework for hybrid system identification, which relies on continuous optimization. This framework is based on the minimization of a cost function that can be chosen as either the minimum or the product of loss functions. The former is inspired by traditional estimation methods, while the latter is inspired by recent algebraic and support vector regression approaches to hybrid system identification. In both cases, the identification problem is recast as a continuous optimization program involving only the real parameters of the model as variables, thus avoiding the use of discrete optimization. This program can be solved efficiently by using standard optimization methods even for very large data sets. In addition, the proposed framework easily incorporates robustness to different kinds of outliers through the choice of the loss function.     

Hybrid singular systems of differential equations

This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced.     

Mixed Tabu machine for portfolio optimization problem

In this paper, we introduce a novel artificial neural network (NN) to solve the portfolio optimization problem. The proposed NN is called the Mixed Tabu Machine (MTM) since its structure is similar to the Tabu Machine, but includes both discrete and continuous variables. Similar to the Hopfield network, the state of the MTM is updated to find the global minimum energy state. To escape from local minimum states of the energy in the MTM, the state transition mechanism is controlled by a Tabu search in both discrete and continuous search spaces. The experimental results for five standard benchmark data sets show that the MTM can clearly obtain good results in very small computation time.     

一类不确定脉冲型混杂系统的保代价控制

针对混合代价函数,研究了参数不确定脉冲型混杂系统的保代价控制问题,给出了混杂状态反馈保代价控制律的设计方法,由此得到的控制律既能使系统闭环鲁棒渐近稳定,又可使系统的闭环混合代价指标在对象参数摄动的范围内不超过确定的上界.本文提出的控制律不仅包含连续时间动态,也包含离散事件动态,而且其离散事件动态行为不需要与被控系统的离散事件动态行为一致,因此设计时不要求被控系统的每个连续时间子系统都具有可控性.仿真结果表明所提设计方法是可行有效的.     

Finite abstractions for hybrid systems with stable continuous dynamics

This paper outlines an abstraction process in which a particular class of hybrid automata with continuous dynamics that have parameterized positive limit sets, are being abstracted into finite transition systems. The limit sets with their corresponding attraction regions define pre- and post-conditions for the continuous dynamics, and determine the transitions in the discrete abstraction. An observable (weak) bisimulation equivalence is established between the two models. The abstraction process described can find application in verification, as well as in planning and symbolic control.     

Time-optimal control for discrete-time hybrid automata

In this paper, the problem of time-optimal control for hybrid systems with discrete-time dynamics is considered. The hybrid controller steers all trajectories starting from a maximal set to a given target set in minimum time. We derive an algorithm that computes this maximal winning set. Also, algorithms for the computation of level sets associated with the value function rather than the value function itself are presented. We show that by solving the reachability problem for the discrete time hybrid automata we obtain the time optimal solution as well. The control synthesis is subject to hard constraints on both control inputs and states. For linear discrete-time dynamics, linear programming and quantifier elimination techniques are employed for the backward reachability analysis. Emphasis is given on the computation of operators for non-convex sets using an extended convex hull approach. A two-tank example is considered in order to demonstrate the techniques of the paper.     

Polyhedral Flows in Hybrid Automata

A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete updates with differential constraints for capturing continuous flows. Formal verification of hybrid automata relies on symbolic fixpoint computation procedures that manipulate sets of states. These procedures can be implemented using boolean combinations of linear constraints over system variables, equivalently, using polyhedra, for the subclass of linear hybrid automata. In a linear hybrid automaton, the flow at each control mode is given by a rate polytope that constrains the allowed values of the first derivatives. The key property of such a flow is that, given a state-set described by a polyhedron, the set of states that can be reached as time elapses, is also a polyhedron. We call such a flow a polyhedral flow. In this paper, we study if we can generalize the syntax of linear hybrid automata for describing flows without sacrificing the polyhedral property. In particular, we consider flows described by origin-dependent rate polytopes, in which the allowed rates depend, not only on the current control mode, but also on the specific state at which the mode was entered. We identify necessary and sufficient conditions for a class of flows described by origin-dependent rate polytopes to be polyhedral. We also propose and study additional classes of flows: strongly polyhedral flows, in which the set of states that can be reached up to a given time starting from a polyhedron is guaranteed to be a polyhedron, and polyhedrally sliced flows, in which the set of states that can be reached at a given time starting from a polyhedron is guaranteed to be a polyhedron. Finally, we discuss an application of the above classes of flows to approximate exponential behaviours.     

混杂系统的虚拟对象实验室平台建设

通过对混杂系统典型实例即三水箱系统特性的分析,从系统安全的角度讨论了用于控制该系统离散状态切换序列的基于混杂自动机描述的贪婪型与周期型控制策略.依据此控制策略,利用VC＋＋与Matlab的混合编程技术开发了该混杂系统的虚拟对象实验室平台.通过对三水箱系统及仿真环境参数的设置,此平台不仅可以形象地演示虚拟对象在不同初始条件下的混杂特性,而且可以实现预定的控制策略并进行仿真研究,从而为具有此类混杂特性的混杂系统的深入研究,提供了一个虚拟的实验环境.