Jose B. Cruz

Stable Cooperative Surveillance With Information Flow Constraints

We consider a cooperative surveillance problem for a group of autonomous air vehicles (AAVs) that periodically receives information on suspected locations of targets from a satellite and then must cooperate to decide which AAV should search for each target. This cooperation must be performed in spite of imperfect intervehicle communications (e.g., messages with random but bounded delays), less than full communication connectivity between vehicles, uncertainty in target locations, and imperfect vehicle search sensors. We represent the state of the search progress with a ldquosearch map,rdquo and use an invariant set to model the set of states where there is no useful information on target locations. Arrivals of new suspected target location information from the satellite corresponds to perturbations of the search map from this invariant set. A cooperation strategy that pursues a type of ldquopersistent area denialrdquo will try to force trajectories of the system into the invariant set by exploiting initial target information and search progress by the AAVs. We show that the invariant set is exponentially stable for a class of cooperative surveillance strategies. We provide a comparative analysis of cooperative and noncooperative strategies. Next, we show via simulations the impact of imperfect communications, imperfect vehicle search sensors, uncertainty in search locations, and pop-up suspected locations on performance.

Market monitoring and control of ancillary services

Abstract In this paper, the problems of market monitoring and control of ancillary services of future energy systems are presented. We envision that future system operation of electric power systems will evolve into completely unbundled ancillary service markets that are governed by spot price signals. The grid operators need to acquire ancillary services through competitive markets for control of the system operation. With the above vision of the future, this paper presents the control of ancillary services based on a frequency regulation/load following (LFC) market, a load regulating (RL) market, and a base load (BL) market. In the LFC market, the units dispatched for generation must have specific response characteristics as determined by the nature of system loads. These units will be controlled by the grid operator. It is envisioned that LFC will be multi-time scale and decentralized. In the RL market, the units dispatched for generation will not participate in LFC. These units are dispatched for specific period of time for regulating system load. The BL units are dispatched daily to satisfy the BL of the day on a weekly or monthly basis. The locational market power associated with generators participating in LFC and in RL is even more critical than that for generators participating in satisfying the BL, since these units are required for frequency regulation, voltage support and relief of overload conditions. To create an efficient market for these services, we will propose and formulate the use of incentive strategies for the BL, RL and the LFC markets.

Adaptive State Feedback Nash Strategies for Linear Quadratic Discrete-Time Games

Abstract A substantial effort has been devoted to various adaptive techniques of systems. Most of these concepts work in the control domain, where every system only has one controller. Yet, for the multi-controller counterpart — dynamic games, adaptations are usually considered from a perspective of systems, for an example, evolutionary games. In this paper, we propose a new adaptive approach for linear quadratic discrete-time games with scalar inputs and state feedback Nash strategies. We consider the effort of adaptation under a Fictitious Play (FP) framework with learning algorithms derived from conventional adaptive control methods. Convergence to Nash strategies is proved with the condition that there exists a unique state feedback strategy, which implies that the associated coupled discrete-time algebraic Riccati equations (DAREs) have a unique positive semi-definite solution. The requirement of Persistency of Excitation (PE) is satisfied by proper reference signals to be tracked.

Asymptotic ε-Nash Equilibrium for 2nd Order Two-Player Nonzero-sum Singular LQ Games with Decentralized Control

Abstract We propose a new equilibrium concept: asymptotic e-Nash equilibrium for 2***nd order two-player nonzero-sum games where each player has a control-free cost functional quadratic in the system states over an infinite horizon and each players control strategy is constrained to be continuous linear state feedback. Based on each players singular control problem, the asymptotic e-Nash equilibrium implemented by partial state feedback is constructed and the feedback gains can be found by solving a group of algebraic equations which involves the system coefficients and weighting matrices in the cost functionals. As an illustration of the theories discussed in this paper, a numerical example is given where the partial state feedback gains can be found explicitly in terms of the system coefficients and weighting matrices in the cost functionals.

Enforcing Incentives in Multilevel Leader-Follower Sliding Mode Strategies

Abstract For a single follower with a convex cost it has been shown that an affine incentive can he used to influence the follower into accepting the leaders global optimal solution as the team solution. This paper extends those results to systems with multiple followers by outlining conditions under which a set of affine incentives can be enforced simultaneously. Tests are given for the static case to check if the leader can enforce incentives based either on hypersurfaces or half-spaces, and the hypersurface test is extended into the dynamic case. The choice of sliding surfaces for the dynamic case is also discussed.

Game of Defending a Target: A Linear Quadratic Differential Game Approach

Abstract Pursuit-evasion (PE) differential games have recently received much attention in military applications involving adversaries. We extend the PE game problem to a problem of defending target, where the roles of the players are changed. The evader is to attack some fixed target, whereas the pursuer is to defend the target by intercepting the evader. We propose a practical strategy design approach based on the linear quadratic game theory with a receding horizon implementation. We prove the existence of solutions for the Riccati equations associated with games with simple dynamics. Simulation results justify the method.