Abstract
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.
Highlights
Neural networks have provided an ideal framework for online identification and control of many complex uncertain engineering systems because of their great flexibility in approximating a large class of continuous maps and their adaptability due to their inherently parallel architecture
Compartmental systems involve dynamical models that are characterized by conservation laws e.g., mass and energy capturing the exchange of material between coupled macroscopic subsystems known as compartments
We extend the results of 2 to develop a neuroadaptive control framework for discrete-time nonlinear uncertain nonnegative and compartmental systems
Summary
Neural networks have provided an ideal framework for online identification and control of many complex uncertain engineering systems because of their great flexibility in approximating a large class of continuous maps and their adaptability due to their inherently parallel architecture. Even though neuroadaptive control has been applied to numerous engineering problems, neuroadaptive methods have not been widely considered for problems involving systems with nonnegative state and control constraints 1, 2. We extend the results of 2 to develop a neuroadaptive control framework for discrete-time nonlinear uncertain nonnegative and compartmental systems. Since in certain applications of nonnegative and compartmental systems e.g., pharmacological systems for active drug administration control source inputs as well as the system states need to be nonnegative, we develop neuroadaptive controllers that guarantee the control signal as well as the physical system states remain nonnegative for nonnegative initial conditions.
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