The analysis and proper documentation of the properties of closed-loop control software presents many distinct aspects from the analysis of the same software running open-loop. Issues of physical system representations arise, and it is desired that s
uch representations remain independent from the representations of the control program. For that purpose, a concurrent program representation of the plant and the control processes is proposed, although the closed-loop system is sufficiently serialized to enable a sequential analysis. While dealing with closed-loop system properties, it is also shown by means of examples how special treatment of nonlinearities extends from the analysis of control specifications to code analysis.
A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a steady-state m
easurement cost. The sensors can switch between systems instantaneously, and there are additional resource constraints, for example on the number of sensors which can observe a given system simultaneously. We first derive a tractable relaxation of the problem, which provides a bound on the achievable performance. This bound can be computed by solving a convex program involving linear matrix inequalities. Exploiting the additional structure of the sites evolving independently, we can decompose this program into coupled smaller dimensional problems. In the scalar case with identical sensors, we give an analytical expression of an index policy proposed in a more general context by Whittle. In the general case, we develop open-loop periodic switching policies whose performance matches the bound arbitrarily closely.
As the digital world enters further into everyday life, questions are raised about the increasing challenges brought by the interaction of real-time software with physical devices. Many accidents and incidents encountered in areas as diverse as medic
al systems, transportation systems or weapon systems are ultimately attributed to software failures. Since real-time software that interacts with physical systems might as well be called control software, the long litany of accidents due to real-time software failures might be taken as an equally long list of opportunities for control systems engineering. In this paper, we are interested only in run-time errors in those pieces of software that are a direct implementation of control system specifications: For well-defined and well-understood control architectures such as those present in standard textbooks on digital control systems, the current state of theoretical computer science is well-equipped enough to address and analyze control algorithms. It appears that a central element to these analyses is Lyapunov stability theory, which translate into invariant theory in computer implementations.
