Neural adaptive control for nonlinear multiple time scale dynamic systems

Adaptive control of nonlinear systems has been an active area in recent years, but it is difficult to control unknown plants. A common approach to deal with this problem is to utilize the simultaneous identification technique. Neural networks have been employed in the identification and control of unknown nonlinear systems owing to their massive parallelism, fast adaptation and learning capability. Neural networks based control naturally leads to problems in nonlinear control and nonlinear adaptive control. The past decade has witnessed great activity in the field, with increased awareness on the part of researchers that such problems can be addressed within the framework of mathematical control theory. Adaptive neural networks control can be classified by the types of neural networks or by methods. By neural networks, we have continuous time [23], discrete-time [2], feedforward [21] and recurrent [16] neuro control. By methods, for examples, internal model neuro control used forward and inverse model are within the feedback loop [25]. Neural control can realize output regulation and tracking problems in nonlinear systems [2], decentralized control for large-scale systems was proposed in [6], backstepping technique can be applied for neural control [24]. Adaptive neural networks control has two kinds of structure: indirect and direct adaptive control. Direct neuro adaptive may realize the neuro control by neural network directly [21]. The indirect method is the combination of the neural network identifier and adaptive control, the controller is derived from the on-line identification [26]. Lyapunov synthesis approach is most popular tool for neural control [22]. Lyapunov–Krasovskii functions can be used for adaptive neural control with unknown time delays [5]. Passivity analysis can simplify the learning algorithms [29]. Some of neural networks applications, such as patterns storage and solving optimization problem, require that the equilibrium points of the designed network be stable [9]. So, it is important to study the stability of neural networks. Dynamic neural networks with different time-scales can model the dynamics of the short-term memory (neural activity levels) and the long-term memory (dynamics of unsupervised synaptic modifications). Their capability of storing patterns as stable equilibrium points requires stability criteria which includes the mu-