Discrete-Time Adaptive State Tracking Control Schemes Using Gradient Algorithms

This paper conducts a comprehensive study of a classical adaptive control problem: adaptive control of a state-space plant model: $\dot{x}(t) = A x(t) + B u(t)$ in continuous time, or $x(t+1) = A x(t) + B u(t)$ in discrete time, for state tracking of a chosen stable reference model system: $\dot{x}_m(t) = A_m x_m(t) + B_m r(t)$ in continuous time, or $x_m(t+1) = A_m x_m(t) + B_m r(t)$ in discrete time. Adaptive state tracking control schemes for continuous-time systems have been reported in the literature, using a Lyapunov design and analysis method which has not been successfully applied to discrete-time systems, so that the discrete-time adaptive state tracking problem has remained to be open. In this paper, new adaptive state tracking control schemes are developed for discrete-time systems, using a gradient method for the design of adaptive laws for updating the controller parameters. Both direct and indirect adaptive designs are presented, which have the standard and desired adaptive law properties. Such a new gradient algorithm based framework is also developed for adaptive state tracking control of continuous-time systems, as compared with the Lyapunov method based framework

Concurrent Learning Adaptive Model Predictive Control with Pseudospectral Implementation

This paper presents a control architecture in which a direct adaptive control technique is used within the model predictive control framework, using the concurrent learning based approach, to compensate for model uncertainties. At each time step, the control sequences and the parameter estimates are both used as the optimization arguments, thereby undermining the need for switching between the learning phase and the control phase, as is the case with hybrid-direct-indirect control architectures. The state derivatives are approximated using pseudospectral methods, which are vastly used for numerical optimal control problems. Theoretical results and numerical simulation examples are used to establish the effectiveness of the architecture.Comment: 21 pages, 13 figure

Multi-drug infusion control using model reference adaptive algorithm

Control of physiological states such as mean arterial pressure (MAP) has been successfully achieved using single drug by different control algorithms. Multi-drug delivery demonstrates a significantly challenging task as compared to control with a single-drug. Also the patient’s sensitivity to the drugs varies from patient to patient. Therefore, the implementation of adaptive controller is very essential to improve the patient care in order to reduce the workload of healthcare staff and costs. This paper presents the design and implementation of the model reference adaptive controller (MRAC) to regulate mean arterial pressure and cardiac output by administering vasoactive and inotropic drugs that are sodium nitroprusside (SNP) and dopamine (DPM) respectively. The proposed adaptive control model has been implemented, tested and verified to demonstrate its merits and capabilities as compared to the existing research work