We present a method for designing a robust control policy for an uncertain system subject to temporal logic specifications. The system is modeled as a finite Markov Decision Process (MDP) whose transition probabilities are not exactly known but are known to belong to a given uncertainty set. A robust control policy is generated for the MDP that maximizes the worst-case probability of satisfying the specification over all transition probabilities in this uncertainty set. To this end, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming solves for a e-suboptimal robust control policy with time complexity O(log1/e) times that for the non-robust case.

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Robust control of uncertain Markov Decision Processes with temporal logic specifications

Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

Systems should not only be correct but also robust in the sense that they behave reasonably in unexpected situations. This article addresses synthesis of robust reactive systems from temporal specifications. Existing methods allow arbitrary behavior if assumptions in the specification are violated. To overcome this, we define two robustness notions, combine them, and show how to enforce them in synthesis. The first notion applies to safety properties: If safety assumptions are violated temporarily, we require that the system recovers to normal operation with as few errors as possible. The second notion requires that, if liveness assumptions are violated, as many guarantees as possible should be fulfilled nevertheless. We present a synthesis procedure achieving this for the important class of GR(1) specifications, and establish complexity bounds. We also present an implementation of a special case of robustness, and show experimental results.

Synthesizing robust systems

While the importance of robustness in engineering design is well accepted, it is less clear how to design cyber-physical systems (CPS) for robustness. With the objective of developing a robustness theory for CPS, we introduce a notion of robustness for cyber systems inspired by existing notions of input-output stability in control theory. We show that the proposed notion of robustness captures two intuitive goals: bounded disturbances lead to bounded deviations from nominal behavior, and the effect of a sporadic disturbance disappears in finitely many steps. For cyber systems modeled as finite-state transducers, the proposed notion of robustness can be verified in pseudo-polynomial time. The synthesis problem, consisting of designing a controller enforcing robustness, can also be solved in pseudo-polynomial time.

Towards Robustness for Cyber-Physical Systems

ion-based, hierarchical approaches to control synthesis from temporal logic specifications for dynamical systems have gained increased popularity over the last decade Yet various issues commonly encountered and extensively dealt with in control systems have not been adequately discussed in the context of temporal logic control of dynamical systems, such as inter-sample behaviors of a sampled-data system, effects of imperfect state measurements and un-modeled dynamics, and the use of time-discretized models to design controllers for continuous-time dynamical systems We discuss these issues in this paper The main motivation is to demonstrate the possibility of accounting for the mismatches between a continuous-time control system and its various types of abstract models used for control synthesis We do this by incorporating additional robustness measures in the abstract models Such robustness measures are gained at the price of either increased non-determinism in the abstracted models or relaxed versions of the specification being realized Under a unified notion of abstraction, we provide concrete means of incorporating these robustness measures and establish results that demonstrate their effectiveness in dealing with the above mentioned issues

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Abstraction, discretization, and robustness in temporal logic control of dynamical systems

Systems working in uncertain environments should possess a robustness property, which ensures that the behaviours of the system remain close to the original behaviours under the influence of unmodeled, but bounded, disturbances. We present a theory and algorithmic tools for the design of robust discrete controllers for π-regular properties on discrete transition systems. Formally, we define metric automata - automata equipped with a metric on states - and strategies on metric automata which guarantee robustness for π-regular properties. We present graph-theoretic algorithms to construct such strategies in polynomial time. In contrast to strategies computed by classical automata-theoretic algorithms, the strategies computed by our algorithm ensure that the behaviours of the controlled system under disturbances satisfy a related property which depends on the magnitude of the disturbance. We show an application of our theory to the design of controllers that tolerate infinitely many transient errors provided they occur infrequently enough.

Robust discrete synthesis against unspecified disturbances

A key property for systems subject to uncertainty in their operating environment is robustness: ensuring that unmodeled but bounded disturbances have only a proportionally bounded effect upon the behaviors of the system. Inspired by ideas from robust control and dissipative systems theory, we present a formal definition of robustness as well as algorithmic tools for the design of optimally robust controllers for ω-regular properties on discrete transition systems. Formally, we define metric automata—automata equipped with a metric on states—and strategies on metric automata which guarantee robustness for ω-regular properties. We present fixed-point algorithms to construct optimally robust strategies in polynomial time. In contrast to strategies computed by classical graph theoretic approaches, the strategies computed by our algorithm ensure that the behaviors of the controlled system gracefully degrade under the action of disturbances; the degree of degradation is parameterized by the magnitude of the disturbance. We show an application of our theory to the design of controllers that tolerate infinitely many transient errors provided they occur infrequently enough.

A theory of robust omega-regular software synthesis

A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by ideas from robust control and dissipative systems theory, we present a formal definition of robustness and algorithmic tools for the design of optimally robust controllers for omega-regular properties on discrete transition systems. Formally, we define metric automata - automata equipped with a metric on states - and strategies on metric automata which guarantee robustness for omega-regular properties. We present fixed point algorithms to construct optimally robust strategies in polynomial time. In contrast to strategies computed by classical graph theoretic approaches, the strategies computed by our algorithm ensure that the behaviours of the controlled system gracefully degrade under the action of disturbances; the degree of degradation is parameterized by the magnitude of the disturbance. We show an application of our theory to the design of controllers that tolerate infinitely many transient errors provided they occur infrequently enough.

Elaine Render

Papers

Robust discrete synthesis against unspecified disturbances

A theory of robust omega-regular software synthesis

A theory of robust software synthesis