Abstract
In this chapter, we prove the stability of a certain class of nonlinear discrete MIMO (Multi-Input Multi-Output) systems controlled by a multilayer neural net with a simple weight adaptation strategy. The proof is based on the Lyapunov stability theory. However, the stability statement is only valid if the initial weight values are not too far from their optimal values which allow perfect model matching (local stability). We therefore propose to initialize the weights with values that solve the linear problem. This extends our previous work (Renders, 1993; Saerens, Renders & Bersini, 1994), where single-input single-output (SISO) systems were considered.
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Renders, JM., Saerens, M., Bersini, H. (1995). Adaptive Neurocontrol of a Certain Class of MIMO Discrete-Time Processes Based on Stability Theory. In: Hunt, K.J., Irwin, G.R., Warwick, K. (eds) Neural Network Engineering in Dynamic Control Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-3066-6_3
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DOI: https://doi.org/10.1007/978-1-4471-3066-6_3
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