A stable neural control approach for uncertain nonlinear systems

Closed loop system stability is the first requirement of any control system design. Nonlinearity and uncertainty in the dynamics of systems are two issues that can make the design of stable control systems difficult. Nonlinearities can reduce, or eliminate our ability to use tractable linear mathematics and uncertainties can cause us to sacrifice performance in order to insure adequate control over a range of plant behavior. Early application of neural networks to control system design focused on the learning capabilities without formal regard for stability of the closed loop system.; This dissertation investigates the use of neural networks in a control system design framework that guarantees stability. The design method is able to address plants with nonlinearities and bounded uncertainties. Stability is guaranteed as a part of the design process using Lyapunov's second (direct) method. Feed-forward neural networks are used to provide approximations to the uncertain dynamics. Both linear-in-the-parameters and nonlinear-in-the-parameters network structures are used. The uncertainties in the dynamics are considered to be both parametric and non-parametric, and they are allowed to originate in the state dependent quantities of model representations which are affine in the controls.