Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

Abstract

We introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

A Bayesian Perspective on Stochastic Neurocontrol

“…Consequently they proposed a suboptimal dual adaptive control scheme which was proved to give superior performance to that of certainty equivalence based control methods. Other approaches for stochastic uncertain nonlinear control systems have also been developed [8], [17]- [19].…”

“…Designing a probabilistic control method allows, as will be demonstrated in the paper, taking model uncertainty into consideration when designing the near to optimal control law. Taking knowledge of uncertainty into consideration when deriving the near to optimal control gives superior control results [8], [17]- [19].…”

PMAC: probabilistic multimodality adaptive control

“…Historical process data that describes the dynamics of the system to be controlled are analysed by a Bayesian approach to build the mixture model in terms of a linear combination of adaptive dynam-ical kernel functions. The estimation of the proposed probabilistic adaptive control framework is based on the use of mixture density network [Bishop, 1995, Herzallah andLowe, 2003], that is extended and developed in this work to handle uncertain jump systems. This method of estimation is referred to as the multiple mode density network.…”

Towards probabilistic synchronisation of local controllers

“…These attributes make the analysis, estimation and especially control of such systems a significant challenge which has yet to be adequately addressed. Several estimation and control methods have been proposed in the literature, including synchronising chaos Boccaletti et al (2002); Tan et al (2003), pinning control Porfiri & diBernardo (2008), multi-agent control Broek et al (2008), probabilistic control Herzallah (2011); Herzallah & Lowe (2003, 2007, decentralised controlŠiljak & Zečević (2005), and distributed control Wang et al (2014). However, these control techniques suffer from either representing single-agent architectures as far as the controller design is concerned, which are centralised and so complete observation of the global state must be known, or are decentralised and decisions are based only on disconnected knowledge.…”