Unknown Switching Signals Research Articles

Distributed switched model-based predictive control for distributed large-scale systems with switched topology

Distributed switched large-scale systems are composed by dynamically coupled subsystems, in which interactions among subsystems vary over time according a switching signal. This paper presents a distributed robust switched model-based predictive control (DSwMPC) to control such systems. The proposed method guarantees stabilising the origin of the whole closed-loop system and ensures the constraints satisfaction in the presence of an unknown switching signal. In the distributed model-based predictive control (DMPC) used in this work, by considering the interactions among subsystems as an additive disturbance, the effect of the switch is reflected on the dynamic equation, local, and consistency constraint sets of the nominal subsystems. To compensate the effect of switching signal which creates a time-varying network topology, a robust tube-based switched model-based predictive control (RSwMPC) with switch–robust control invariant set as the target set robust to unknown mode switching is used as local controller. The scheme performance is assessed using three typical examples. The simulation results show that the input and state constraints are satisfied by the proposed DSwMPC at all times. They also validate that the closed-loop system converges to the origin. Also, a comparison of the DSwMPC with a centralised SwMPC (CSwMPC) and a decentralised SwMPC (DeSwMPC) are performed.

Decentralized fixed-time uniform ISS stabilization of infinite networks of switched nonlinear systems with arbitrary switchings by small gain approach

We prove a new theorem on ℓ∞-fixed-time uniform ISS decentralized stabilization of infinite networks composed of interconnected switched nonlinear systems with unknown switching signals. Each subsystem has the lower-triangular form with uncontrollable linearization, more specifically, it has the lower-triangular form with the so-called “generalized polynomial integrators”. To solve this problem, we use a new small gain theorem on ℓ∞-fixed-time uniform input-to-state stability of infinite networks and redesign several previous backstepping algorithms of decentralized stabilization. In particular, our main result generalizes several recent related ones.

Switched systems with transient unsustainable modes: Stability and feasibility

Externally switched systems have unique characteristics that make it is especially challenging to ensure their stability and feasibility. These challenges are exacerbated when the system contains modes with uncontrollable dynamics, tight input constraints, and/or unstable dynamics. While past results have addressed stability and feasibility of switched systems, little has been done, thus far, for constrained, switched systems with uncontrollable modes. This work examines linear systems in this context with unknown switching signals that have upper and lower bounds on the duration the system will dwell in a mode and constraints on which modes can be switched between. These constraints create a finite number of different possible switching signal statuses, which depend on the current mode and the time spent dwelling in that mode. At design time, state constraints corresponding to each possible status are computed and, at run-time, are activated based on the switching signal status. If these time-varying state constraints respect certain properties, persistent feasibility, convergence, and exponential stability are established under all possible switching signals. This is later extended to be a sequence of state constraints for use in model predictive control. These results are then demonstrated on two numerical examples.

Fixed‐time fault‐tolerant control of uncertain MIMO switched interconnected systems subject to state delay, unknown control directions, and quantized nonlinear inputs

SummaryThis paper investigates design of an adaptive fixed‐time fault‐tolerant decentralized controller for a class of uncertain multi‐input multi‐output (MIMO) switched large‐scale non‐strict interconnected systems under arbitrary switching subject to unknown control directions, quantized nonlinear inputs, actuator failures unknown external disturbances, and unmodeled dynamics. In addition to interconnected terms, time‐varying delayed interconnected terms have been considered in the system model which makes it more general than previous works in the literature. The proposed controller can handle switched systems with unknown switching signal and different types of input nonlinearities including, saturation, backlash, and dead‐zone. The singularity problem in designing the fixed time controller has been solved. The quantizer and actuators fault parameters are assumed to be unknown. The Razumikhin lemma has been used to deal with the delayed interconnected terms. To cope with the system unknown dynamics, neural networks (NNs) have been applied and by updating the maximum norms of the networks weight vectors the computational load has been reduced. The explosion of complexity occurring in the traditional back‐stepping technique has been avoided by applying dynamic surface control (DSC). Finally, by defining an appropriate common Lyapunov function (CLF), fixed‐time convergence of system outputs and the closed‐loop system stability have been established. The effectiveness of the proposed controller has been shown via simulation study.

Online learning of data-driven controllers for unknown switched linear systems

Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under unknown switching signals. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees stability of the closed-loop switched linear system provided that the switching is slow enough. Effectiveness of the proposed design technique is illustrated for two aerospace applications.

State estimation of Lipschitz continuous switched systems with unknown switching signals

For Lipschitz continuous switched systems the problems of reconstructing the state of the system and of the switching signal are tackled assuming no knowledge of the switching signal, except its dwell time. To do so, algorithms to estimate the switching times and the current mode of the system, were developed that take into account the non-smoothness of the vector fields and the output map of the system. Although an specific state observer model was used in the simulations, the algorithm that reconstructs the switching signal runs irrespective of the state estimator selected.

FEA-based tracking control of flexible body switching dynamic structure

AbstractIn dynamically switched systems with unknown switching signal, the control system is conventionally designed based on the worst switching scenario to ensure system stability. Such conservative design demands excessive control effort in less critical switching configurations. In the case of continuum mechanics systems, such excessive control inputs result in increased structural deformations and resultant modeling uncertainties. These deformations alter differential equations of motion which cripple the task of control. In this paper, a new approach for tracking control of uncertain continuum mechanics multivariable systems undergoing switching dynamics and unknown time delay has been proposed. Control algorithm is constructed based on the mathematical rigid model of the plant and a Common Lyapunov Function (CLF) is proposed upon sliding hyperplane regarding all switching configurations. Considering the model-based nature of sliding mode control (SMC) and inevitable uncertainties induced from modeling simplifications of continuum system or parameter evaluation errors, Finite Element Analysis (FEA) is utilized to approximate total model uncertainties. To obtain robust stability, instead of conventional switching functions in the construction of control law, the control inputs are selected such that system dynamics reside within stability bounds which are calculated based on the Lyapunov asymptotic stability criterion. Therefore, the unwanted chattering issue caused by continuous switching is not observed in control input signals. Eventually, the accuracy of the proposed method has been verified through the student version of ANSYS® mechanical APDL-based simulations and its effectiveness has been demonstrated in multiple operating conditions.

A state estimation strategy for a nonlinear switched system with unknown switching signals

A strategy is presented to estimate the state of a nonlinear autonomous switched system, with no knowledge of the switching signal, except its dwell time. To do so, algorithms to estimate the switching times and the current mode of the system are developed. The estimation of the switching times is based on approximating the second ( generalised) derivative of the output of the system via a convolution of this signal with a suitable function and on detecting the corresponding spikes. To estimate the modes, a scheme based on the use of a bank of observers (one for each mode) and of a bank of subsystems (for each step of the estimation process a suitable subset of the subsystems of the switched system) is developed. The algorithms run regardless of the state observer model, as long as its output error norm decays exponentially with a controlled decay rate.

Estimation in uncertain switched systems using a bank of interval observers: local vs glocal approach

This paper discusses some issues related with the design of a bank of interval observers for uncertain switched systems, in which several sources of uncertainty are considered: parametric uncertainties, unknown disturbances, measurement noise, and unknown switching signal. More specifically, this paper focuses on analyzing the interval estimation accuracy when changes of active mode induce non-positivity of the interval state estimation errors. In particular, it is shown that by combining two types of interval observers, referred to as local and global, the accuracy and reliability of the estimation can be improved. The properties of the obtained so-called glocal observer are investigated and illustrated by means of numerical simulations.

Decentralized uniform input-to-state stabilization of hierarchically interconnected triangular switched systems with arbitrary switchings

We consider a class of large-scale systems composed of hierarchically interconnected switched nonlinear triangular form subsystems affected by external disturbances with arbitrarily varying switching signals. For any system of this class, we design a decentralized feedback controller which renders the entire large-scale closed-loop system globally ISS with respect to the external disturbances uniformly and regardless of the unknown switching signals. To solve the problem, we use a certain modification of the classical small gain theorems formulated in terms of the ISS Lyapunov functions and combine it with our version of the backstepping approach with a suitable gain assignment.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

In this paper, an adaptive neural net- works (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

On the distinguishability and observer design for single-input single-output continuous-time switched affine systems under bounded disturbances with application to chaos-based modulation

Switched Affine Systems (SAS׳s) is a class of Hybrid Systems composed of a collection of Affine Systems (AS׳s) and a switching signal that determines, at each time instant, the evolving affine subsystem. This paper is concerned with the observability and observer design for single-input single-output (SISO) SAS׳s under unknown perturbation, for the case that no information about the switching signal is available. It is firstly demonstrated that in the presence of disturbances every pair of AS׳s is always indistinguishable from the continuous output, meaning that it is not possible to infer the evolving AS by using only the information provided by the output of the SAS. Nevertheless, by taking advantage of the knowledge on the disturbance bound, new distinguishability conditions are derived, making possible to distinguish the evolving AS. By using these new distinguishability conditions, an observer scheme for SISO SAS׳s, subject to unknown switching signal and unknown perturbations, is presented. Such an observer scheme determines in finite-time the evolving AS. Furthermore, it estimates both the state of the system and the disturbance. Finally, the proposed observer scheme is effectively applied for a non-autonomous chaotic modulation application, which is an attractive method for spread-spectrum secure communication in which the message is fed as a disturbance to a chaotic SAS and the output is then transmitted through an open channel to a receiver, which is an observer algorithm that recovers the message (the disturbance) from the output signal.

Stabilizing Model Predictive Control without Terminal Constraints for Switched Nonlinear Systems

Abstract: This work proposes a Model Predictive Control (MPC) approach without terminal constraints for switched nonlinear systems subject to time-dependent and a priori unknown switching signals. Under a controllability assumption, it is shown that the controlled system is asymptotically stable if the switching signal fulfills a certain average dwell time condition. The results are applied to a continuous stirred-tank reactor with two different modes of operation.

On the observer design problem for continuous-time switched linear systems with unknown switchings

The observer design problem for Switched Linear Systems (SLS) subject to an unknown switching signal is addressed in this work. Based on known observability results for SLS, an appropriate SLS observer is proposed and its convergence is analysed showing that the corresponding estimates converge in finite-time to the SLS state. More precisely, the observers of the continuous state evolution and the observers of the switching signal are investigated and their convergence studied separately. The main tool to analyse the observability is the well-known geometric concept of (A, B)-invariant subspaces. The developed SLS observers are then applied to construct synchronized chaotic generators based on the SLS with chaotic behavior. Finally, an example of a non-trivial chaotic SLS and its detailed analysis are presented to illustrate the achieved results.

Robust Output Feedback Stabilization of Switched Nonlinear Systems with Average Dwell Time

AbstractFor some switched nonlinear systems, stabilization can be achieved under arbitrary switching with state feedback control. Due to switching zero dynamics, output feedback stabilization for some switched nonlinear systems needs dwell time between switching to guarantee system stability. In this paper, we consider a class of switched nonlinear systems with unknown parameters and unknown switching signals. We design a robust output feedback controller that stabilizes the system under a class of switching signals with average dwell time (ADT) where the value of ADT can be reduced by adjusting the control gain. For some special cases, common quadratic Lyapunov functions of the closed‐loop systems can be found and the value of ADT is further relaxed. Some examples and simulations are provided to validate the results.

On the Observability of Continuous-Time Switched Linear Systems Under Partially Unknown Inputs

This technical note addresses the problem of observability of continuous-time Switched Linear Systems (SLS) subject to unknown disturbances, unknown switching signals and unconstrained nonzero dwell time. For this class of hybrid systems, a geometric characterization of the observability properties is presented. In particular, attention is focused on the estimation of the SLS state from the continuous measurements. Using the well known concept of (A, B)-invariant subspaces, three main problems are addressed and solved, namely the observability for every nonzero state trajectory, the observability for almost every control input, and the observability for almost every state trajectory. It is also shown that the approach herein presented subsumes some of the classical results on observability of SLS previously reported in the literature, and allows expressing them in a common framework.

Variable Structure Based Adaptive Control with Tuning Function Design for a Class of Unknown Switched Linear Systems

AbstractThis paper considers the control problem of switched linear systems with unknown parameters and unknown switching signals. For the considered system, robust model reference adaptive control (MRAC) approach can only guarantee error boundedness under an average dwell time (ADT) condition which is implicit and is difficult to estimate. We propose a variable structure (VS) based adaptive control with tuning function design to achieve better results than the MRAC approach. Moreover, the VS control is partially extended to relative degree two case and using similar approach, it can be generalized to higher relative degree case.