State-Space Quantization Design for the Suboptimal Control of Constrained Systems Using Neuromorphic Controllers

During the last few years there has been considerable interest in the use of trainable controllers based upon the use of neuron-like elements, with the expectation being that these controllers can be trained, with relatively little effort, to achieve good performance. However, good performance hinges on the ability of the neural net to generate a "good" control law even when the input does not belong to the training set, and it has been shown that neural-nets do not necessarily generalize well. It has been proposed that this problem can be solved by essentially quantizing the state-space and then using a neural-net to implement a table look-up procedure. However, there is little information on the effect of this quantization upon the controllability properties of the system. In this paper we address this problem by extending the theory of control of constrained systems to the case where the controls and measured states are restricted to finite or countably infinite sets. These results provide the theoretical framework for recently suggested neuromorphic controllers but they are also valuable for analyzing the controllability properties of computer-based control systems

Norm Based Optimally Robust Control of Constrained Discrete Time Linear Systems

Most realistic control problems involve both some type of time-domain constraints and model uncertainty. However, the majority of controller design procedures currently available focus only on one aspect of the problem, with only a handful of method capable of simultaneously addressing, albeit in a limited fashion, both issues. In this paper we propose a simple design procedure that takes explicitly into account both time domain constraints and model uncertainty. Specifically, we use a operator norm approach to define a simple robustness measure for constrained systems. The available degrees of freedom are then used to optimize this measure subject to additional performance specifications. We believe that the results presented here provide a useful new approach for designing controllers capable of yielding good performance under substantial uncertainty while meeting design constraints

A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics

Finite horizon model reduction and the appearance of dissipation in Hamiltonian systems

An apparent paradox in classical statistical physics is the mechanism by which conservative, time-reversible microscopic dynamics, can give rise to seemingly dissipative behavior. In this paper we use system theoretic tools to show that dissipation can arise as an artifact of incomplete observations over a finite horizon. In addition, this approach allows us to obtain finite-time, low order, approximations of systems with moderate size and to establish how the approach to the thermodynamic limit depends on the different physical parameters

Benchmark problems for robust control design

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76996/1/AIAA-20949-475.pd

CONTROLLABILITY OF LINEAR IMPULSE DIFFERENTIAL SYSTEMS

We give necessary and sufficient conditions for global controllability of stationary and non-stationary linear impulse differential control systems on a fixed interval. I

A convex optimization approach to synthesizing bounded complexity lλ filters

We consider the worst-case estimation problem in the presence of unknown but bounded noise. Contrary to stochastic approaches, the goal here is to confine the estimation error within a bounded set. Previous work dealing with the problem has shown that the complexity of estimators based upon the idea of constructing the state consistency set (e.g., the set of all states consistent with the a priori information and experimental data) cannot be bounded a priori, and can, in principle, continuously increase with time. To avoid this difficulty we propose a class of bounded complexity filters, based upon the idea of confining $r$length error sequences (rather than states) to hyperrectangles. The main result of the technical note shows that this can be accomplished by using linear time invariant filters of order no larger than $r$. Further, synthesizing these filters reduces to a combination of convex optimization and line search. © 2006 IEEE