Control Of Continuous-time Nonlinear Systems Research Articles

Adaptive control of nonlinear continuous-time systems using neural networks—General relative degree and MIMO cases : Fu-Chuang Chen, Chen-Cheng Liu, pp 901–904

Abstract Multilayer neural networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback linearizable continuous-time system with relative degree ≥ 1. The single-input/single-output system is studied first and then the methodology is extended to control square multi-input/multi-output systems. The control objective is for the plant to track a reference trajectory, nd the control law is defined in terms of the outputs of the neural networks. he parameters of the networks are updated on-line according to an augmented tracking error and the network derivatives. local convergence theorem is given on he convergence of the tracking error and its derivatives, nd the norm of the parameter error vectors. his control algorithm is applied to control a two-input/two-output relative-degree-two system.

Adaptive control of non-linear continuous-time systems using neural networks—general relative degree and MIMO cases

Multilayer neural networks are used in a non-linear adaptive control problem. The plant is an unknown feedback linearizable continuous-time system with relative degree 1. The single-input:/single-output system is studied first and then the methodology is extended to control square multi-input/multi-output systems. The control objective is for the plant to track a reference trajectory, and the control law is defined in terms of the outputs of the neural networks. The parameters of the networks are updated on-line according to an augmented tracking error and the network derivatives. A local convergence theorem is given on the convergence of the tracking error. This control algorithm is applied to control a two-input/two-output relative-degree-two system.

Adaptive Control of Nonlinear Continuous-Time Systems Using Neural Networks - General Relative Degree and MIMO Cases

Multilayer neural networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback linearizable continuous-time system with relative degree ≥ 1. The single-input/single-output system is studied first and then the methodology is extended to control square multi-input/multi-output systems. The control objective is for the plant to track a reference trajectory, nd the control law is defined in terms of the outputs of the neural networks. he parameters of the networks are updated on-line according to an augmented tracking error and the network derivatives. local convergence theorem is given on he convergence of the tracking error and its derivatives, nd the norm of the parameter error vectors. his control algorithm is applied to control a two-input/two-output relative-degree-two system.

Discrete-time control of continuous-time non-linear systems

A rigorous gain scheduling approach is developed to design non-linear state-feedback controllers for sampled continuous-time non-linear systems. All the information needed in the design can be obtained from measurements of the continuous-time plant about selected equilibrium points. The performance of the resulting controllers is explored using two examples

A Modified Gradient Procedure for Adaptation in Nonlinear Control Systems

A modified gradient procedure is proposed for making discrete-time changes in the adjustable parameters of a continuous-time nonlinear control system during normal operating conditions. The algorithm employs the best available estimate of the unknown plant parameters as well as the estimates of disturbance, state, and output variables. The importance of the metric properties of a performance index is discussed, and the necessary and sufficient conditions for the integral squared error index to possess metric properties are derived. Theoretical conditions for the error correctiveness of the algorithm are formulated in terms of the constrained extrema of quadratic functionals.