doi:10.1155/2008/868425 Research Article Neural Network Adaptive Control for Discrete-Time Nonlinear Nonnegative Dynamical Systems

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences, and they typically involve the exchange of nonnegative quantities between subsystems or compartments, wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a neuroadaptive control framework for adaptive set-point regulation of discrete-time nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions. Copyright q 2008 Wassim M. Haddad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1

Data-Driven Feedback Linearization of Nonlinear Systems with Periodic Orbits in the Zero-Dynamics

In this article, we present data-driven feedback linearization for nonlinear systems with periodic orbits in the zero-dynamics. This scenario is challenging for data-driven control design because the higher order terms of the internal dynamics in the discretization appear as disturbance inputs to the controllable subsystem of the normal form. Our design consists of two parts: a data-driven feedback linearization based controller and a two-part estimator that can reconstruct the unknown nonlinear terms in the normal form of a nonlinear system. We investigate the effects of coupling between the subsystems in the normal form of the closed-loop nonlinear system and conclude that the presence of such coupling prevents asymptotic convergence of the controllable states. We also show that the estimation error in the controllable states scales linearly with the sampling time. Finally, we present a simulation based validation of the proposed data-driven feedback linearization

Optimal discrete-time control for non-linear cascade systems

In this paper we develop an optimality-based framework for designing controllers for discrete-time nonlinear cascade systems. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping-type controllers parameterized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Bellman equation for the controlled system and thus guarantees both optimality and stability

VECTOR DISSIPATIVITY THEORY FOR DISCRETE-TIME LARGE-SCALE NONLINEAR DYNAMICAL SYSTEMS

In analyzing large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper, we develop an analysis framework for discrete-time large-scale dynamical systems based on vector dissipativity notions. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the discrete-time composite large-scale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. In particular, extended Kalman-Yakubovich-Popov conditions, in terms of the subsystem dynamics and interconnection constraints, characterizing vector dissipativeness via vector system storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for discrete-time large-scale nonlinear dynamical systems using vector Lyapunov functions. 1

Adaptive controls and anesthesiology: Is there a future?

Abstract only availableDuring a patient's surgery, an anesthesiologist has to periodically adjust controls on drug-delivery machines to keep a patient's consciousness at a desired level (a BIS value between 40 and 60). If this physician did not have to adjust these controls, he or she would be able to devote more time during the surgery on a patient's life functions instead of on the patient's level of consciousness. To help with this endeavor, I developed a simulation that uses algorithms developed by Professor Chellaboina and his coworkers to adjust a patient's BIS value to 50. To construct this model, I used a computer program called Simulink, a component of MATLAB, to make the necessary connections between functions so the algorithms could work. When this simulation was run, the BIS value did reach 50; however, this only occurred under ideal conditions: when a disturbance was not added to the model. When a disturbance was added to this simulation, unacceptable levels of oscillation occurred. I believe this disturbance is coming from the EEG device (used to calculate the BIS value) that is used to monitor a patient's level of consciousness. Before this model could be clinically used, either an improvement in the EEG device or a program that could counteract this disturbance would need to be developed. Effort will be made to derive preliminary control designs to account for this disturbance.NSF-REU Biosystems Modelin

Finite Settling Time Control of the Double Integrator Using a Virtual Trap-Door Absorber

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57813/1/TrapDoorTAC2000.pd

Dissipativity theory and stability of feedback interconnections for hybrid dynamical systems

In this paper we develop a unified dynamical systems framework for a general class of systems possessing left-continuous flows; that is, left-continuous dynamical systems. These systems are shown to generalize virtually all existing notions of dynamical systems and include hybrid, impulsive, and switching dynamical systems as special cases. Furthermore, we generalize dissipativity, passivity, and nonexpansivity theory to left-continuous dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to left-continuous dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy, dissipated energy over the continuous-time dynamics, and dissipated energy over the resetting events. Finally, the generalized dissipativity notions are used to develop general stability criteria for feedback interconnections of left-continuous dynamical systems. These results generalize the positivity and small gain theorems to the case of left-continuous, hybrid, and impulsive dynamical systems

A unification between nonlinear-nonquadratic optimal control and integrator backstepping

In this paper we develop an optimality-based framework for backstepping controllers. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees both optimality and stability. The results are specialized to the case of integrator backstepping

Computing zero deficiency realizations of kinetic systems

In the literature, there exist strong results on the qualitative dynamical properties of chemical reaction networks (also called kinetic systems) governed by the mass action law and having zero deficiency. However, it is known that different network structures with different deficiencies may correspond to the same kinetic differential equations. In this paper, an optimization-based approach is presented for the computation of deficiency zero reaction network structures that are linearly conjugate to a given kinetic dynamics. Through establishing an equivalent condition for zero deficiency, the problem is traced back to the solution of an appropriately constructed mixed integer linear programming problem. Furthermore, it is shown that weakly reversible deficiency zero realizations can be determined in polynomial time using standard linear programming. Two examples are given for the illustration of the proposed methods. © 2015 Elsevier B.V. All rights reserved