Nonlinear System Stabilisation by an Evolutionary Neural Network
This paper presents the application of an evolutionary neural network controller in a stabilisation problem involving an inverted pendulum. It is guaranteed that the resulting continuous closed-loop system is asymptotically stable. The process of training the neural network controller can be treated as a constrained optimisation problem where the equality constraint is derived from the Lyapunov stability criteria. The decision variables in this investigation are made up from the connection weights in the neural network, a positive definite matrix required for the Lyapunov function and a matrix for the stability constraint while the objective value is calculated from the closed-loop system performance. The optimisation technique chosen for the task is a variant of genetic algorithms called a cooperative coevolutionary genetic algorithm (CCGA). Two control strategies are explored: model-reference control and optimal control. In the model-reference control, the simulation results indicate that the tracking performance of the system stabilised by the evolutionary neural network is superior to that controlled by a neural network, which is trained via a neural network emulator. In addition, the system stabilised by the evolutionary neural network requires the energy in the level which is comparable to that found in the system that uses a linear quadratic regulator in optimal control. This confirms the usefulness of the CCGA in nonlinear system stabilisation applications.
KeywordsNeural Network Connection Weight Linear Quadratic Regulator Stability Constraint Neural Network Controller
Unable to display preview. Download preview PDF.
- 13.Ekachaiworasin, R., Kuntanapreeda, S.: A Training Rule which Guarantees Finite-Region Stability of Neural Network Closed-Loop Control: An Extension to Nonhermitian Systems. In: Amari, S.-I., Giles, C.L., Gori, M., Piuri, V. (eds.) Proceedings of the 2000 IEEE-INNS-ENNS International Joint Conference on Neural Networks, pp. 325–330. IEEE Computer Society, Los Alamitos (2000)Google Scholar
- 15.Potter, M.A., De Jong, K.A.: A Cooperative Coevolutionary Approach to Function Optimization. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 249–257. Springer, Heidelberg (1994)Google Scholar
- 16.De Jong, K.A., Potter, M.: Evolving Complex Structures via Cooperative Coevolution. In: McDonnell, J.R., Reynolds, R.G., Fogel, D.B. (eds.) Proceedings of the Fourth Annual Conference on Evolutionary Programming, pp. 307–318. MIT Press, Cambridge (1995)Google Scholar
- 17.Potter, M.A., De Jong, K.A.: Evolving Neural Networks with Collaborative Species. In: Ören, T.I., Birta, L.G. (eds.) Proceedings of the 1995 Summer Computer Simulation Conference, pp. 340–345. Society for Computer Simulation, San Diego (1995)Google Scholar