A stochastic PID controller for a class of MIMO systems

This paper deals with the design of a controller possessing tracking capability of any realisable reference trajectory while rejecting measurement noise. We consider discrete-time-varying multi-input multi-output stable linear systems and a proportional-integral-derivative (PID) controller. A novel recursive algorithm estimating the time-varying PID gains is proposed. The development of the proposed algorithm is based on minimising a stochastic performance index. The implementation of the proposed algorithm is described and boundedness of trajectories and convergence characteristics are presented for a discretised continuous-time model. Simulation results are included to illustrate the performance capabilities of the proposed algorithm.     

Robust dynamic programming for min-max model predictive control of constrained uncertain systems

We address min-max model predictive control (MPC) for uncertain discrete-time systems by a robust dynamic programming approach, and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The method uses polyhedral representations of the cost-to-go functions and feasible sets, and performs multiparametric programming by a duality based approach in each recursion step. We show how to apply the method to robust MPC, and give conditions guaranteeing closed loop stability. Finally, we apply the method to a tutorial example, a parking car with uncertain mass.     

A new decentralized implicit adaptive regulator for large-scale systems described by discrete-time state-space mathematical models

In this paper, we treat the problem of decentralized implicit adaptive regulation for large-scale stochastic systems composed into a set of interconnected systems that are described by discrete-time state-space mathematical models with unknown parameters. The key idea in the decentralized regulation method is to design local regulator using only local information such that the state of each interconnected system is regulated to a certain constant reference signal. The main contribution is the proposition of a decentralized implicit adaptive regulator based on state-feedback strategy that can be applied to stochastic interconnected systems with unknown parameters. Furthermore, the practical implementation of the proposed decentralized implicit adaptive regulator can be made easily (low-cost implementation of the electronic components, short computation of the decentralized control law, etc.). A theorem is established and proved which gives sufficient stability conditions of the resulting closed-loop interconnected systems by using the Lyapunov method. An example of numerical simulation is treated to test the performance of the proposed decentralized implicit adaptive regulator.     

Simultaneously stabilizing controller design for a class of MIMO systems

It is shown that a class of linear, time-invariant, multi-input multi-output plants can be simultaneously stabilized. This class of plants all have the same number of zeros at infinity, at zero, or both, but no other zeros in the unstable region. If they have zeros at zero or infinity, then their gain matrices at zero and infinity also satisfy a positive-definiteness condition. There is no restriction on the poles of the plants considered in this class. An explicit design procedure is proposed to achieve simultaneously stabilizing controllers. All simultaneously stabilizing controllers for this class of plants are also characterized in terms of a parameter matrix that satisfies a unimodularity condition.     

A disturbance rejection self-tuning controller for a class of MIMO non-minimum phase systems

This paper is concerned with the problem of disturbance rejection in an adaptive controller design. A new adaptive control algorithm is derived to obtain the complete measurable disturbance rejection both in dynamic and static states for a class of non-minimum phase MIMO systems by reassigning the system zeros to the stable region     

A state-space approach to parameterization of stabilizingcontrollers for nonlinear systems

A state-space approach to the Youla parameterization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parameterized output feedback controllers have separation structures. This machinery allows the parameterization of stabilizing controllers to be conducted directly in state space without using coprime factorization     

A unified approach to a state-space model for linear distributed systems†

A state-space model for a class of linear distributed-parameter systems has been obtained. The method is based on the eigenfunction integration approach to the system and provides a unified approach to linear distributed systems with both laterally distributed and variable boundary controls. The method is illustrated by a one-dimensional diffusion process.     

Adaptive fuzzy controller design with observer for a class of uncertain nonlinear MIMO systems

In this paper, an adaptive fuzzy control approach is proposed to stabilize a class of uncertain nonlinear MIMO systems with the unmeasured states and the external disturbances. The fuzzy logic systems are used to approximate the unknown functions. Because it does not required to assume that the system states are measurable, it needs to design an observer to estimate the system unmeasured states. The considered MIMO systems are more general, i.e. they consist of N subsystems and each subsystem is in the non‐affine form. The stability of the closed‐loop system is verified by using Lyapunov analysis method. Two simulation examples are utilized to verify the effectiveness of the proposed approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems

In this work, we present a novel adaptive fault tolerant control (FTC) scheme for a class of control input and system state constrained multi‐input multi‐output (MIMO) nonlinear systems with both multiplicative and additive actuator faults. The input constraints can be asymmetric, and the state constraints can be time‐varying. A novel tan‐type time‐varying Barrier Lyapunov Function (BLF) is proposed to deal with the state constraints, and an auxiliary system is designed to analyze the effect of the input constraints. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small neighbourhood of zero is guaranteed, while the constraints on the system state will not be violated during operation. Estimation errors for actuator faults are bounded in the closed loop. An illustrative example on a two degree‐of‐freedom robotic manipulator is presented to demonstrate the effectiveness of the proposed FTC scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

A variable structure convex programming based control approach for a class of uncertain linear systems

A variable structure convex programming based control for a class of linear uncertain systems with accessible state is presented in this note. A convex programming problem is solved, on-line, by reformulating the problem in terms of a piecewise smooth penalty function, and relying on a suitable analog variable structure system implementing the gradient procedure. In this way, the controlled system reference movement, optimal with respect to a pre-specified scalar convex cost function and a set of suitable equality and inequality constraints, is generated. An inner control loop aimed at the finite time exact tracking of the reference movement is also designed. As a result, the controlled system trajectory starting in the feasible region there remains, and the optimal movement in the feasible region is proved to be an asymptotically stable equilibrium point of the controlled system.     

A state-space approach to Walsh series solution of linear systems

A state-space procedure for solving linear dynamic systems by the Walsh series is developed. A new operational matrix plays the main role and a new Kronecker product formula is established. The laborious use of Corrington'B tables is eliminated. Several examples illustrate the process and demonstrate the power of the approach.     

Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems

In this paper, an adaptive iterative learning controller (AILC) with input learning technique is presented for uncertain multi-input multi-output (MIMO) nonlinear systems in the normal form. The proposed AILC learns the internal parameter of the state equation as well as the input gain parameter, and also estimates the desired input using an input learning rule to track the whole history of command trajectory. The features of the proposed control scheme can be briefly summarized as follows: 1) To the best of authors’ knowledge, the AILC with input learning is first developed for uncertain MIMO nonlinear systems in the normal form; 2) The convergence of learning input error is ensured; 3) The input learning rule is simple; therefore, it can be easily implemented in industrial applications. With the proposed AILC scheme, the tracking error and desired input error converge to zero as the repetition of the learning operation increases. Single-link and two-link manipulators are presented as simulation examples to confirm the feasibility and performance of the proposed AILC.

     

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.     

A simple robust controller for a class of nonlinear systems

A new robust state‐feedback controller is designed to solve the tracking problem of a class of nonlinear uncertain systems. The contributions of our paper are threefold: Firstly, a new robust state‐feedback controller with a simple structure is derived. Owing to its simplicity, less computation is needed. What is more, for polynomial‐type uncertainties, a much simpler controller can be derived directly without the need of computing partial derivatives. Secondly, a technique that leaves positive functions used in the nonlinear damping terms to be chosen freely is introduced which may enable us to find out a good one among all candidate positive functions to reduce the control effort and to design a ‘softer’ controller. Thirdly, the assumption made in non‐adaptive robust control schemes where the bounding functions are required to be exactly known is relaxed, and the assumption on the reference signal is relaxed too. When our robust controller is applied, the simulations show that better performance can be achieved with less control effort. Copyright © 2000 John Wiley & Sons, Ltd.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

A universal iterative learning stabilizer for a class of MIMO systems

Design of iterative learning control (ILC) often requires some prior knowledge about a system's control matrix. In some applications, such as uncalibrated visual servoing, this kind of knowledge may be unavailable so that a stable learning control cannot always be achieved. In this paper, a universal ILC is proposed for a class of multi-input multi-output (MIMO) uncertain nonlinear systems with no prior knowledge about the system control gain matrix. It consists of a gain matrix selector from the unmixing set and a learned compensator in a form of the positive definite discrete matrix kernel, corresponding to rough gain matrix probing and refined uncertainty compensating, respectively. Asymptotic convergence for a trajectory tracking within a finite time interval is achieved through repetitive tracking. Simulations and experiments of uncalibrated visual servoing are carried out in order to verify the validity of the proposed control method.     

Output recurrent wavelet neural network-based adaptive backstepping controller for a class of MIMO nonlinear non-affine uncertain systems

In this paper, an adaptive backstepping control problem is proposed for a class of multiple-input-multiple-output nonlinear non-affine uncertain systems. An output recurrent wavelet neural network (ORWNN) is used to approximate the unknown nonlinear functions to develop the proposed adaptive backstepping controller. The proposed ORWNN combines the advantages of wavelet-based neural network, fuzzy neural network, and output feedback layer to achieve higher approximation accuracy and faster convergence. According to the estimation of ORWNN, the control scheme is designed by backstepping approach such that the system outputs follow the desired trajectories. Based on the Lyapunov approach, our approach guarantees that the system outputs converge to a small neighborhood of the references signals, that is, all signals of the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results including double pendulums system and two inverted pendulums on carts system are shown to demonstrate the performance and effectiveness of our approach.     

A structural approach to detectability for a class of hybrid systems

We address detectability of linear switching systems. We show that detectability of a linear switching system reduces to asymptotic stability of a suitable switching system with guards extracted from it. A condition for checking asymptotic stability of linear switching systems with guards is also derived.     

基于未建模动态补偿的一类MIMO非线性系统的自适应广义预测解耦切换控制

针对一类不确定的多输入多输出(MIMO)离散时间零动态不稳定非线性系统, 提出了一种基于未建模动态补偿的非线性广义预测解耦切换控制方法. 该控制方法要求系统的未建模动态满足线性增长条件, 放宽了未建模动态全局有界的限制. 建立了所提的自适应控制方法的稳定性和收敛性分析. 而且, 在设计广义预测解耦控制器时, 把“一一映射”与ANFIS的训练相结合来估计系统的未建模动态, 保证了ANFIS的万能逼近特性. 最后, 仿真结果验 证了所提方法的优越性.