Biblio

We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The abstraction is related to the concrete control system via a so-called simulation function: a Lyapunov-like function, which is used to establish a quantitative bound between the behavior of the approximate abstraction and the concrete system. In the first part of the paper, we provide a small gain type condition that facilitates the compositional construction of an abstraction of an interconnected control system together with a simulation function from the abstractions and simulation functions of the individual subsystems. In the second part of the paper, we restrict our attention to linear control system and characterize simulation functions in terms of controlled invariant, externally stabilizable subspaces. Based on those characterizations, we propose a particular scheme to construct abstractions for linear control systems. We illustrate the compositional construction of an abstraction on an interconnected system consisting of four linear subsystems. We use the abstraction as a substitute to synthesize a controller to enforce a certain linear temporal logic specification.

Zero dynamics attack is lethal to cyber-physical systems in the sense that it is stealthy and there is no way to detect it. Fortunately, if the given continuous-time physical system is of minimum phase, the effect of the attack is negligible even if it is not detected. However, the situation becomes unfavorable again if one uses digital control by sampling the sensor measurement and using the zero-order-hold for actuation because of the `sampling zeros.' When the continuous-time system has relative degree greater than two and the sampling period is small, the sampled-data system must have unstable zeros (even if the continuous-time system is of minimum phase), so that the cyber-physical system becomes vulnerable to `sampling zero dynamics attack.' In this paper, we begin with its demonstration by a few examples. Then, we present an idea to protect the system by allocating those discrete-time zeros into stable ones. This idea is realized by employing the so-called `generalized hold' which replaces the zero-order-hold.

Autonomous active exploration requires search algorithms that can effectively balance the need for workspace coverage with energetic costs. We present a strategy for planning optimal search trajectories with respect to the distribution of expected information over a workspace. We formulate an iterative optimal control algorithm for general nonlinear dynamics, where the metric for information gain is the difference between the spatial distribution and the statistical representation of the time-averaged trajectory, i.e. ergodicity. Previous work has designed a continuous-time trajectory optimization algorithm. In this paper, we derive two discrete-time iterative trajectory optimization approaches, one based on standard first-order discretization and the other using symplectic integration. The discrete-time methods based on first-order discretization techniques are both faster than the continuous-time method in the studied examples. Moreover, we show that even for a simple system, the choice of discretization has a dramatic impact on the resulting control and state trajectories. While the standard discretization method turns unstable, the symplectic method, which is structure-preserving, achieves lower values for the objective.

We consider the problem of robust on-line optimization of a class of continuous-time nonlinear systems by using a discrete-time controller/optimizer, interconnected with the plant in a sampled-data structure. In contrast to classic approaches where the controller is updated after a fixed sufficiently long waiting time has passed, we design an event-based mechanism that triggers the control action only when the rate of change of the output of the plant is sufficiently small. By using this event-based update rule, a significant improvement in the convergence rate of the closed-loop dynamics is achieved. Since the closed-loop system combines discrete-time and continuous-time dynamics, and in order to guarantee robustness and semi-continuous dependence of solutions on parameters and initial conditions, we use the framework of hybrid set-valued dynamical systems to analyze the stability properties of the system. Numerical simulations illustrate the results.

In this paper, we focus on the principal-agent problems in continuous time when the participants have ambiguity on the output process in the framework of g-expectation. The first best (or, risk-sharing) type is studied. The necessary condition of the optimal contract is derived by means of the optimal control theory. Finally, we present some examples to clarify our results.

Distributed optimization is an emerging research topic. Agents in the network solve the problem by exchanging information which depicts people's consideration on a optimization problem in real lives. In this paper, we introduce two algorithms in continuous-time to solve distributed optimization problems with equality constraints where the cost function is expressed as a sum of functions and where each function is associated to an agent. We firstly construct a continuous dynamic system by utilizing the Lagrangian function and then show that the algorithm is locally convergent and globally stable under certain conditions. Then, we modify the Lagrangian function and re-construct the dynamic system to prove that the new algorithm will be convergent under more relaxed conditions. At last, we present some simulations to prove our theoretical results.

In this paper, we consider distributed algorithm based on a continuous-time multi-agent system to solve constrained optimization problem. The global optimization objective function is taken as the sum of agents' individual objective functions under a group of convex inequality function constraints. Because the local objective functions cannot be explicitly known by all the agents, the problem has to be solved in a distributed manner with the cooperation between agents. Here we propose a continuous-time distributed gradient dynamics based on the KKT condition and Lagrangian multiplier methods to solve the optimization problem. We show that all the agents asymptotically converge to the same optimal solution with the help of a constructed Lyapunov function and a LaSalle invariance principle of hybrid systems.