Compositional abstraction and safety synthesis using overlapping symbolic models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

Learning-based Symbolic Abstractions for Nonlinear Control Systems

Symbolic models or abstractions are known to be powerful tools towards the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach towards the construction of symbolic models for nonlinear control systems. In particular, the symbolic model is constructed based on learning the un-modeled part of the dynamics from training data based on state-space exploration, and the concept of an alternating simulation relation that represents behavioral relationships with respect to the original control system. Moreover, we aim at achieving safe exploration, meaning that the trajectory of the system is guaranteed to be in a safe region for all times while collecting the training data. In addition, we provide some techniques to reduce the computational load of constructing the symbolic models and the safety controller synthesis, so as to make our approach practical. Finally, a numerical simulation illustrates the effectiveness of the proposed approach

Backstepping controller synthesis and characterizations of incremental stability

Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descriptions of incremental stability in terms of existence of coordinate-invariant notions of incremental Lyapunov functions and contraction metrics, respectively. Most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks: they can only be applied to control systems in either parametric-strict-feedback or strict-feedback form, and they require these control systems to be smooth. In this paper, we propose a design technique that is applicable to larger classes of (not necessarily smooth) control systems. Moreover, we propose a recursive way of constructing contraction metrics (for smooth control systems) and incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems, the approximation of stochastic hybrid systems, source-code model checking for nonlinear dynamical systems and so on. The effectiveness of the proposed results in this paper is illustrated by synthesizing a controller rendering a non-smooth control system incrementally stable as well as constructing its finite abstraction, using the computed incremental Lyapunov function.Comment: 23 pages, 2 figure

Fully symbolic-based technique for solving complex state-space control systems

Despite the superiority of symbolic approaches over the purely numerical approaches in many aspects, it does not receive the proper attention due to its significant complexity, high resources requirement and long drawn time which even grows significantly with the increase of model dimensions. However, its merits deserve every attempt to overcome the difficulties being faced. In this paper, a fully generic symbolic-based technique is proposed to deal with complex state space control problems. In this technique, depending on the model dimension if exceeds a predefined limit, the state space is solved using the partitioned matrices theory and block wise inversion formula. Experimental results demonstrate that the proposed technique overcomes all the previously mentioned barriers and gives the same results when compared to numerical methods (Simulink). Moreover, it can be used to gain useful information about the system itself, provides an indication of which parameters are more important and reveals the sensitivity of system model to single parameter variations