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We consider the problem of computing parameters of player cost functionals such that given state and control trajectories constitute an open-loop Nash equilibrium for a noncooperative differential game. We propose two methods for solving this inverse differential game problem and novel conditions under which our methods compute unique cost-functional parameters. Our conditions are analogous to persistence of excitation conditions in adaptive control and parameter estimation. The efficacy of our methods is illustrated in simulations. [ABSTRACT FROM AUTHOR]

This note brings together stability and optimality theory to design distributed cooperative control protocols that guarantee consensus and are globally optimal with respect to a positive semi-definite quadratic performance criterion. A common problem in cooperative optimal control is that global optimization problems generally require global information, which is not available to distributed controllers. Optimal control for multi-agent systems is complicated by the fact that the communication graph topology interplays with the agent system dynamics. In the note we use an inverse optimality approach together with partial stability to consider the cooperative consensus and pinning control. Agents with identical linear time-invariant dynamics are considered. Communication graphs are assumed directed and having fixed topology. Structured quadratic performance indices are derived that capture the topology of the graph, which allows for global optimal control that is implemented using local distributed protocols. A new class of digraphs is defined that admits a distributed solution to the global optimal control problem, namely those with simple graph Laplacian matrices. [ABSTRACT FROM AUTHOR]

The attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method. The adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals. This is achieved by the inverse optimality approach, without solving the associated Hamilton-Jacobi-Isaacs partial differential (HJIPD) equation directly. The design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping, and a control Lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve H∞ disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy. The convergence of adaptive parameters is also analyzed in terms of invariant manifold. Numerical simulations illustrate the performance of the proposed control algorithms. [ABSTRACT FROM AUTHOR]