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 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.     

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.     

Stability analysis of a multiple-model controller for constrained uncertain nonlinear systems

This paper outlines the construction and the analysis of a multiple-model-based controller in order to deal with the stability of uncertain systems subject to constraints on its state and its control. It is assumed that the process can be defined by a finite number of models. The multiple-model approach is first formally introduced, and then the stability analysis is performed by using the vector norms and overvaluing model frameworks. We demonstrate through original theorems how the multiple-model approach improves the sizes of the stability and attractive subsets first when only one model is sufficient to represent the process and then when a collection of its models is used.     

Observer design for a class of MIMO nonlinear systems

A simple observer is proposed for a large class of MIMO nonlinear systems which includes many physical models. The main characteristic of the proposed observer lies in the easiness of its implementation and calibration. Indeed, the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given. Moreover, its calibration is achieved through the choice of a single parameter. A simulation example is given in order to illustrate the performance of the proposed observer.     

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.     

A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems

A hybrid indirect and direct adaptive fuzzy output tracking control schemes are developed for a class of nonlinear multiple-input-multiple-output (MIMO) systems. This hybrid control system consists of observer and other different control components. Using the state observer, it does not require the system states to be available for measurement. Assisted by observer-based state feedback control component, the adaptive fuzzy system plays a dominant role to maintain the closed-loop stability. Being the auxiliary compensation, H/sup /spl infin// control and sliding mode control are designed to suppress the influence of external disturbance and remove fuzzy approximation error, respectively. Thus, the system performance can be greatly improved. The simulation results demonstrate that the proposed hybrid fuzzy control system can guarantee the system stability and also maintain a good tracking performance.     

A new approach for designing a reduced-order controller of linearsingular systems

An approach for designing a multivariable reduced-order controller of a linear, time-invariant, singular system is presented. The approach is based on decomposing the original system into slow and fast subsystems using the Drazin inverse technique. The resulting subsystems are then used to obtain an observer of reduced order. This, in turn, it used in designing a new reduced-order controller which is capable of placing the dominant eigenvalues of the system in arbitrary locations. The technique is shown to overcome some difficulties inherent in other treatments of reduced-order controllers of singular systems and assures that the known corresponding controller of the regular state-space systems is merely a special case of the present results     

A self-tuning fuzzy controller for a class of multi-input multi-output nonlinear systems

This paper presents a systematic design procedure of a multivariable fuzzy controller for a general Multi-Input Multi-Output (MIMO) nonlinear system with an input-output monotonic relationship or a piecewise monotonic relationship for each input-output pair. Firstly, the system is modeled as a Fuzzy Basis Function Network (FBFN) and its Relative Gain Array (RGA) is calculated based on the obtained fuzzy model. The proposed multivariable fuzzy controller is constructed with two orthogonal fuzzy control engines. The horizontal fuzzy control engine for each system input-output pair has a hierarchical structure to update the control parameters online and compensate for unknown system variations. The perpendicular fuzzy control engine is designed based on the system RGA to eliminate the multivariable interaction effect. The resultant closed-loop fuzzy control system is proved to be passive stable as long as the augmented open-loop system is input-output passive. Two sets of simulation examples demonstrate that the proposed fuzzy control strategy can be a promising way in controlling multivariable nonlinear systems with unknown system uncertainties and time-varying parameters.     

Disturbance decoupling for a class of nonlinear MIMO systems by static measurement feedback

In this paper, the disturbance decoupling problem for a square-invertible nonlinear system is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback. The results are valid for left-invertible systems as well.