Switched Affine System Research Articles

A study on switched affine system interconnected with fast LTI dynamics

We study an interconnection between a switched affine system and a fast LTI dynamics. Often, the classical stabilization method based on the existence of a stable convex combination is directly used for systems on two time scales while using only the slow dynamics. Here, we provide conditions for checking the Uniform Ultimate Boundedness when the fast dynamics is taken into account. In addition, criteria for verifying asymptotical stability are provided for a special case. Numerical examples illustrate the main results.

Lyapunov-Based Policy Synthesis for Multi-Objective Interval MDPs

In this paper, we provide an analysis of the convergence characteristics of the dynamic programming value iteration method based on stability-theoretical results of discrete-time switched affine systems. For interval Markov decision processes subject to multiple objective functions, we reformulate the value iteration algorithm as a switched affine system with additive uncertainties. Building on this change of perspective, we adopt a Lyapunov-based strategy for designing a control policy by finding a switching law that stabilizes the system towards an invariant set of attraction centered at a desired target value. The results provide insights into the convergence of the value iteration algorithm and the feasibility of desired target values. The results are demonstrated on two case studies.

On the Construction of the Graph of Discrete States of a Switched Affine System

The problem of constructing the graph of states of a switched affine system closed by a static state feedback is considered. To solve this problem, a constructive algorithm based on the study of the consistency of systems of linear algebraic inequalities is proposed.

On the Construction of the Graph of Discrete States of a Switched Affine System

On the Construction of the Graph of Discrete States of a Switched Affine System

Double-Layer Optimization of Industrial-Park Energy System Based on Discrete Hybrid Automaton

Combing advanced measurement infrastructure (AMI) and information and communications technology (ICT), the Internet of Things (IoT) has been widely used in the energy system. The continuous state modeling method cannot effectively deal with the various operation scenarios in the park multiple energy system. This paper proposes a hybrid state system modeling method based on the discrete hybrid automaton (DHA). The DHA-based model judges the equipment mode through the logical discriminant and describes the energy transmission process of the equipment with a switched affine system. And a doublelayer optimization structure for the multiple energy system is proposed, which combine the long-term forecasting data and short-term forecasting data. Based on the advanced measurement infrastructure, the forecasting system predicts the system state and determines the scheduling plan of each equipment. This paper uses a typical industrial park case with multiple energy system to verify advantages of the DHA-based modeling method, calculates the economic benefits brought by the optimization and evaluates the maximum carbon emission reduction capacity of the industrial park.

On the Stability of a Switched Affine System for a Class of Switching Signals

We study the problem of stability of the zero equilibrium of a switched affine system closed by a linear static state feedback. The concept of feasible control for a given set of switching signals is introduced, and a constructive condition for checking this property for an arbitrary linear feedback is obtained. A sufficient condition for the stability of the zero equilibrium of a switched affine system closed by a feasible control is formulated.

On the Stability of a Switched Affine System for a Class of Switching Signals

On the Stability of a Switched Affine System for a Class of Switching Signals

A Practically Stabilizing Model Predictive Control Scheme for Switched Affine Systems

This letter presents the design and analysis of a practically stabilizing model predictive control (MPC) scheme for a class of discrete-time switched affine systems with at least one stable subsystem. A pruning algorithm with cost approximation is proposed to ensure the practical stability of the MPC scheme while reducing the online computations. A criterion for selecting the pruning parameters to ensure the feasibility of the MPC scheme is presented, which is formulated as a convex optimization problem. With the proposed pruning, the value function of the MPC scheme becomes a practical-Lyapunov function which guarantees global practical stability of the switched affine system for arbitrary prediction horizons. The MPC scheme is applied to switching power converters and simulation results are given for a buck converter which is a DC-DC converter.

Periodic Time-Triggered Hybrid Control for DC–DC Converter Based on Switched Affine System Model

The introduction of the switched affine system opens new perspectives for the control design of dc–dc converters. In order to overcome the drawbacks of the continuous-time switching control methods, several sampled-data-based switching control approaches have been proposed in the literature. However, in these works, the solution of control parameters involves a nonlinear optimization problem. In addition, the designed switching laws are nonlinear functions about the system state, which require higher computational resources. In this article, a periodic time-triggered hybrid control is proposed based on a new design framework. All the design conditions are in linear matrix inequality formulations, which can be conveniently solved by common semidefinite programming software. Moreover, the proposed switching law is a linear function about the state, reducing the online computing burden. Finally, a unified view of the classical continuous-time switching scheme and the proposed method is established. Simulation and experiment tests on a buck–boost converter demonstrate the good performance of the proposed control strategy.

Output-Based Robust Switching Rule Design for Uncertain Switched Affine Systems: Application to DC–DC Converters

This brief presents a new output-based robust switching control rule for switched affine systems based on observer-based feedback control or dynamic output feedback control. The designed switching rule can drive the state of the switched affine system, which have various equilibrium points, to a desired one, and overcome the effects caused by the parameter uncertainty and external disturbance. The stability conditions for the closed-loop systems are established by applying a common Lyapunov function and are presented in the form of linear matrix inequalities. Finally, physical experiments in a DC-DC boost converter circuit illustrate the effectiveness of the proposed control method.

Integrated fault estimation and tolerant control for discrete-time switched affine systems with mixed switching laws

This study is concerned with the issues of simultaneous actuator fault estimation and the design of observer-based fault-tolerant control for a class of discrete-time switched affine systems subject to a mixed switching scheme. A mixed switching law, which is composed of constant dwell-time and state-dependent switching logic, is introduced to avoid the chattering phenomenon of augmented error switched affine system, and a discretized Lyapunov function approach is used to ensure the asymptotic stability of error systems. Then, the simultaneous fault estimation and tolerant control based state observer are studied and the corresponding design problem is transformed into resolving a multi-objective optimization for augmented error systems with H∞ performance index. Moreover, the gains of fault estimator and tolerant controller are explicitly calculated via resolving the conditions of linear matrix inequalities. Finally, a practical application of DC motor/Buck–Boost converter is illustrated to verify the effectiveness and practicability of the developed approach.

About switched affine system interconnected with fast LTI dynamics

We study an interconnection between a slow switched affine system and a fast LTI system. The lower dimensional slow and fast subsystems are computed via the singular perturbation approach. We consider the classical stabilization method based on the existence of a stable convex combination (while ignoring the fast dynamics) and we provide an LMI condition for checking ultimate boundedness when the fast dynamics is taken into account. Numerical example illustrates the main result.

A Lyapunov-based version of the value iteration algorithm formulated as a discrete-time switched affine system

In this paper, we analyse the convergence properties of the Dynamic Programming Value Iteration algorithm by exploiting the stability theory of discrete-time switched affine systems. More specifically, by formulating the Value Iteration algorithm as a switched affine system, a Lyapunov-based optimal policy selection strategy is designed to guarantee the practical stabilisation of the resulting system towards an invariant set of attraction containing a given target value function. The switching control algorithm, referred to as Lyapunov-based Value Iteration algorithm, can be regarded as a convergence analysis tool and can be adopted to verify if and how such target value function can be approached by choosing from a subset of suitable stationary policies, at each time slot. The usage of the proposed algorithm in practice is also discussed. Finally, two different applications are provided to further illustrate and examine the key-aspects of the approach presented.

Practical stability for switched affine systems via time‐dependent switching function

AbstractIn this article, the stability analysis of both continuous‐time switched affine systems discrete‐time switched affine systems is addressed via dwell time switching. Since the information of system states is difficult to obtain in the state‐dependent switching function, the time‐dependent switching function is considered to stabilize the switched affine system. The purpose of this article is to design a time‐dependent switching function assuring the state trajectories are globally attracted to an attractive set containing the desired equilibrium point (which is selected from a set of attainable equilibrium points). By constructing discretized Lyapunov function, a set of conditions in the framework of dwell time are designed to guarantee practical stability of the state trajectories. At last, some numerical examples are given to illustrate our method and compare it with the existing results.

Dynamic Output Feedback Control of Discrete-Time Switched Affine Systems

This brief focuses on stability analysis and dynamic output feedback controller design for switched affine systems in the discrete-time domain. The main purpose is to design a full order switched affine controller together with a switching function assuring global practically stability of the desired equilibrium points for switched affine systems. The set of all reachable equilibrium points is given. Since the system states information is difficult to obtain, the dynamic output feedback switching function is considered to stabilize the switched affine system. By using the Lyapunov stability theory and linear matrix inequality (LMI) technique, a set of dynamic output feedback gains together with a switching function are designed assuring the practical stability of the desired equilibrium points. At last, numerical examples are proposed to illustrate our approach.

Stabilization of networked switched affine systems with event-triggered strategy

Using an event-based switching law, we address the stability issue for continuous-time switched affine systems in the network environment. The state-dependent switching law in terms of the region function is firstly developed. We combine the region function with the event-triggering mechanism to construct the switching law. This can provide more candidates for the selection of the next activated subsystem at each switching instant. As a result, it is possible for us to activate the appropriate subsystem to avoid the sliding motion. The Zeno behavior for the switched affine system can be naturally ruled out by guaranteeing a positive minimum inter-event time between two consecutive executions of the event-triggering threshold. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Robust sampled-data control for direct current to direct current converters via switched affine description and error tracking strategy

In this article, a novel sampled-data control method is proposed for direct current to direct current converter. According to its switching property, the direct current to direct current converter is described as a switched affine system. A novel error tracking switching law is designed based on the multi-Lyapunov functions method and sampled-data control strategy with variant sampling intervals. The sufficient condition concerning the state of the constructed switched affine system converging to a finite region is developed, which guarantees the outcome voltage can approach the desired value and achieve the voltage adjustment. Based on it, the condition under uncertain parameters is developed as well, which would be more desirable in applications. The effectiveness of the proposed method is verified by numerical simulations. The proposed method is also applicable to other types of power converters.

Multi‐rate sampled‐data control of switched affine systems

This study considers the practical stabilisation of switched affine systems under the multi-rate sampled-data switching control. In order to depict the sampled value of all state components, a sensing block composed of several sensors with asynchronous uncertain non-uniform sampling intervals is applied. On the basis of the sampled-data value, a new class of functionals is developed, which is composed of a Lyapunov–Krasovskii functional and a looped function. Practical stabilisation conditions are presented for the switched affine system by means of a switching law. Two examples are provided to demonstrate the effectiveness and feasibility of the proposed results.

Event-triggered Control for Switched Affine Linear Systems

Event-triggered control problem for switched affine linear systems with a state-dependent switching law is addressed in this paper. By constructing a piecewise differential Lyapunov function with time-scheduled matrices, an event-triggered scheme and a switching signal are proposed. The switching signal depends on the state of the trigger instant. A sufficient condition is developed to ensure that the switched affine system exponentially convergences to a small neighborhood of the desired equilibrium point. The proposed result is then generated to a disturbance attenuation performance analysis. The results are presented in the form of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed results.

Sampled-Data Control With Adjustable Switching Frequency for DC–DC Converters

In this paper, a novel sampled-data control approach is proposed for dc–dc converters. The dc–dc power electronic converter is modeled as a sampled-data switched affine system according to the status of the power switch. A novel switching control algorithm is synthesized by using the switched Lyapunov theory. The proposed approach is able to not only drive the output to a prescribed set point from any initial condition, but also track a varying reference signal, and the switching frequency can be adjusted online with the guaranteed stability. In addition, with this approach, continuous conduction mode and discontinuous conduction mode operations can be treated in a unified way. The effectiveness and merits of the proposed method are illustrated by experiments on a laboratory prototype.