Control Scheme For Linear Systems Research Articles

Tube-based model predictive control for linear systems with bounded disturbances and input delay

This paper proposes a tube-based model predictive control strategy for linear systems with bounded disturbances and input delay to ensure input-to-state stability. Firstly, the actual disturbed system is decomposed into a nominal system without disturbances and an error system. For the nominal system, solving an optimization problem, where the delayed control input is set as an optimization variable, yields a nominal control law that enables the nominal state signal to approach to zero. Then, for the error system, the Razumikhin approach is used to identify a robust control invariant set. Using the set invariance theorem, an ancillary control law is developed to confine the error state signal in the invariant set. Combining the two results, we obtain a control law that enables the state signal to remain within a robustly invariant tube. Finally, the effectiveness of the developed control strategy is validated by simulations.

Chaos Addresses Energy in Networks of Electrical Oscillators

In this paper, a new application of active chaos is presented. It will be shown how chaotic behavior allows to address the energy transport in networks of linear oscillators. The paper is focused on RLC oscillators coupled in a network through links implemented by capacitors. The capacitances are subjected to an external input which leads to fluctuations in their values. This creates the conditions for the onset of decoherence, a situation in which a phenomenon called environment-assisted quantum transport occurs in quantum mechanics. From numerical and experimental observations, the use of active chaos to alter the value of the coupling capacitances reveals to be more effective than the use of random fluctuations. This implies that an energy control strategy for linear systems based on chaos can be outlined.

Metzler matrix-based switching control scheme for linear systems with prescribed performance guarantees

This paper investigates the issue of control design for linear systems with prescribed performance. The novelty of the proposed solution relies on a switching control scheme that uses the interval theory. Different from the existing prescribed performance control approaches, the error transformation and the logarithmic/tangent function are no longer required in the presented control. Alternatively, a switching scheme inspired by the interval observer technique is introduced to ensure the errors not violating performance bound functions. The proposed control establishes an unified prescribed performance control framework which covers the bounded stability, asymptotic stability and finite-time stability only via selecting the corresponding performance bound functions. Numerical examples are simulated to demonstrate the effectiveness of the proposed approach.

Output feedback robust MPC for linear systems with norm-bounded model uncertainty and disturbance

This paper presents an output feedback robust model predictive control strategy for linear systems with norm-bounded model parametric uncertainty and disturbance. In order to reduce the computational burden and enhance the control performance, in the optimization problem we optimize the estimator state matrix instead of the state estimator gain. The infinite horizon control moves and estimated states are parameterized by a dynamic output feedback control law, where its state feedback gain and estimator state matrix are optimized at each sampling instant. By appropriately refreshing the estimation error set, the optimization problem is shown to be recursively feasible and the convergence of the augmented state is guaranteed. A numerical example is given to show the effectiveness of the proposed approach.

Actuator fault tolerant control based on probabilistic ultimate bounds

In this work we introduce a novel set-based fault tolerant control scheme for linear systems under Gaussian disturbances. In the proposed strategy, actuator faults are detected and diagnosed when residual trajectories enter and remain in certain sets that are computed as probabilistic ultimate bounds. After a fault is diagnosed, the control scheme is reconfigured to take into account the corresponding actuator failure and preserve certain closed loop features. We show that our strategy can detect and diagnose the different faults considered with an arbitrarily small probability of misdetection.

Optimal Control of Linear Systems With Limited Control Actions: Threshold-Based Event-Triggered Control

We consider a finite-horizon linear-quadratic optimal control problem where only a limited number of control messages are allowed for sending from the controller to the actuator. To restrict the number of control actions computed and transmitted by the controller, we employ a threshold-based event-triggering mechanism that decides whether or not a control message needs to be calculated and delivered. Due to the nature of threshold-based event-triggering algorithms, finding the optimal control sequence requires minimizing a quadratic cost function over a nonconvex domain. In this paper, we first provide an exact solution to this nonconvex problem by solving an exponential number of quadratic programs. To reduce computational complexity, we then propose two efficient heuristic algorithms based on greedy search and the alternating direction method of multipliers technique. Later, we consider a receding horizon control strategy for linear systems controlled by event-triggered controllers, and we further provide a complete stability analysis of receding horizon control that uses finite-horizon optimization in the proposed class. Numerical examples testify to the viability of the presented design technique.

Robust Output Feedback Model Predictive Control: A Stochastic Approach

AbstractThis paper addresses the robust explicit model predictive control scheme for linear systems with input and output constraint in the presence of disturbances and noise. Conditions for disturbance rejection are established by incorporating a full state/disturbance observer. The separation principle is applied to design an optimal observer in the unconstrained problem. Then, an efficient algorithm is developed to explicitly design observer gains by minimizing a quadratic performance criterion. It is shown that the solution includes a set of regions with piecewise affine functions of the state and reference vectors and a set of regions with optimal observers. In the proposed method, two sets of partitions associated with the control law and the observer gains are obtained. Therefore, the online computation includes finding the active regions of both observer and control law partitions in which the current state is located. The proposed technique is particularly attractive for a wide range of practical problems where the exact model of the actual system is not available.

Networked control design for coalitional schemes using game-theoretic methods

In this work, we present an iterative design method for a coalitional networked control scheme for linear systems. In this scheme, the links in the communication network are enabled or disabled depending on their contribution to the overall system performance. Likewise, the control law is adapted to these changes. In particular, new conditions are included at the design phase, in order to consider constraints on the links and the agents regarding the game theoretical tools utilized while optimizing the matrices that define the controller.

Observer‐based event‐triggered control co‐design for linear systems

The paper deals with an observer-based event-triggered control strategy for linear systems using only local (that is available) variables. Sufficient conditions based on linear matrix inequalities (LMI) associated to convex optimization problems are proposed to ensure the asymptotic stability of the closed loop and the output convergence to a constant reference in both emulation and co-design contexts. Indeed, the proposed approach allows either to design the event-triggering rules or co-design the event-triggering rule along with the controller gain.

Fault tolerant control using adaptive output integral-type sliding mode

This paper proposes a novel fault tolerant control scheme for linear systems with unknown bounded uncertainty and time-varying fault. In this scheme, adaptive output integral-type sliding mode is incorporated with adaptive unknown input observer to cope with aforementioned systems using only input and output information. More specifically, the adaptive unknown input observer is exploited to estimate state and fault simultaneously, and the adaptive output integral-type sliding mode is designed to attenuate unknown bounded uncertainty and tolerate time-varying fault. Then, Lyapunov stability theory is applied to synthesize the design of the observer and nominal controller. Finally, the effectiveness of the proposed method is verified by a numerical example.

Fault-tolerant control for uncertain linear systems via adaptive and LMI approaches

ABSTRACTThis paper proposes a fault-tolerant control scheme for linear systems with mismatched uncertainties which are assumed to be norm-bounded, affine and polytopic, respectively. The linear fractional transformation (LFT) and linear matrix inequality (LMI) techniques are introduced to handle the mismatched uncertainties, and the adaptive techniques are used to compensate actuator faults. By using the cone complementary linearisation algorithm, the resulting stability criteria are converted into solvable ones. Then, on the basis of Lyapunov stability theory, it is shown that the solutions to the closed-loop system and error system are uniformly bounded, especially, the states converge asymptotically to zero. Finally, simulations are given to illustrate the effectiveness and advantages of the proposed theoretical results.

A stabilizing control scheme for linear systems on controlled invariant sets

We present a new stabilizing control scheme for linear discrete-time systems with input and state constraints. Essentially, we seek a controller that is able to steer all initial states within a controlled invariant set towards the origin without violating the constraints. The control law builds on a predictive control scheme. We show that a prediction horizon of n steps, where n denotes the dimension of the system, is sufficient to solve the described control task. The proposed controller is related to but different from established feedback laws associated with λ-contractive sets. In fact, the new control scheme successfully stabilizes systems, where classical λ-contractive control laws fail.

Cooperative economic model predictive control for linear systems with convex objectives

In this paper we propose a cooperative distributed economic model predictive control strategy for linear systems which consist of a finite number of coupled subsystems. The suggested feedback strategy is generating control input which converges to a set of Nash equilibria of the corresponding game provided infinite iterations are allowed at each sampling time. Moreover, the control for each subsystem is computed in itself without coordination layer except for a synchronization requirement between subsystems.We first introduce distributed linear systems with two subsystems and economic model predictive control, then show the convergence and stability properties of a suboptimal model predictive control strategy for the system. The optimization problem for the implementation of MPC is stated with a terminal equality constraint and a terminal cost.

Improved State Space Model Predictive Control Design for Linear Systems with Partial Actuator Failure

This paper presents a new state space model predictive control scheme for linear systems with partial actuator faults. To consider dealing with the uncertainties caused by actuator faults, the proc...

An Iterative Design Method for Coalitional Control Networks with Constraints on the Shapley Value

In this work, we introduce a new iterative design method for a coalitional control scheme for linear systems recently proposed. In this scheme, the links in the network infrastructure are enabled or disabled depending on their contribution to the overall system performance. As a consequence, the local controllers are divided dynamically into sets or coalitions that cooperate in order to attain their control tasks. The new design method allows the control system designer to include new constraints regarding the game theoretical tools of the control architecture, while optimizing the matrices that define the controller.

Resilient Control under Denial-of-Service

We investigate resilient control strategies for linear systems under Denial-of-Service (DoS) attacks. By DoS attacks we mean interruptions of communication on measurement (sensor-to-controller) and control (controller-to-actuator) channels carried out by an intelligent adversary. We characterize the duration of these interruptions under which stability of the closed-loop system is preserved. The resilient nature of the control descends from its ability to adapt the sampling rate to the occurrence of the DoS.

Robust Stabilization for a Class of Uncertain Nonlinear Systems via a Novel Hybrid Control Applicable to Mechanical Systems

An important consideration in control system design is that of model uncertainty. Besides, systems with mixed uncertainties, chaotic vibrations, and input nonlinearities are not easily stabilized and traditional control schemes for linear systems are not always effective. Therefore, in this paper, we will solve two problems, first searching a novel hybrid control methodology to achieve the practical stabilization for uncertain systems with mixed uncertainties and second calculating the guaranteed exponential convergence rate with the convergence radius. The applicability of the main results is demonstrated by a tracking controller design for a class of uncertain nonlinear mass-damper-spring systems with mixed uncertainties, chaotic vibrations, and input nonlinearities.

Multi-Object Control of Active Suspension Subject to Parameter Uncertainties under Non-Stationary Running

Based on the building of non-stationary road surface excitation mode, a study on the active suspension control under non-stationary running condition was conducted using control, state feedback control strategy for linear systems with time-domain hard constraints was propose. The proposed approach was applied to design active suspension systems on the basis of a two-degree-of-freedom quarter car mode, Simulation results show that the proposed constrained controller can achieve a promising improvement on ride comfort, while keeping dynamic suspension deflections, dynamic tire loads and control forces within given bounds, even non-stationary running.

Deadbeat Control for Linear Systems with Input Constraints

A new deadbeat control scheme for linear systems with input constraints is presented. Input constraints exist in most control systems, but in conventional dead-beat control, logical strategy to handle it has not been studied enough. The proposed controller in this paper adjusts the number of steps for dead-beat tracking on-line, in order to achieve delayed deadbeat-tracking performance and satisfy any admissible input constraint. Increasing the number of steps for dead-beat tracking and formulating the corresponding degree of freedom into null-space vectors make it possible to obtain delayed dead-beat tracking, and minimize the inevitable delay, respectively. LMI feasibility problems are solved to numerically obtain the solution and minimize the unavoidable step-delay. As a result, calculation effort is reduced compared to LMI-optimization problem. The proposed schemes can be readily numerically implemented. Its practical usefulness is validated by simulation for 6-axis robot model and experimental results for DC-motor servoing.

Deadbeat Control for Linear Systems with State Constraints

This paper presents a deadbeat control scheme for linear systems with state constraints. The proposed controller increases the number of steps on-line for the deadbeat tracking performance, satisfying given admissible state constraints. LMI conditions are given to minimize the unavoidable step delay. The proposed schemes can be easily developed by using LMI approach, and are validated by numerical simulation.