solve_feedback_lq_game.h

/*
 * Copyright (c) 2019, The Regents of the University of California (Regents).
 * All rights reserved.
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 *       notice, this list of conditions and the following disclaimer.
 *
 *    2. Redistributions in binary form must reproduce the above
 *       copyright notice, this list of conditions and the following
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 *       with the distribution.
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 *    3. Neither the name of the copyright holder nor the names of its
 *       contributors may be used to endorse or promote products derived
 *       from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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 * Please contact the author(s) of this library if you have any questions.
 * Authors: David Fridovich-Keil   ( dfk@eecs.berkeley.edu )
 */

///////////////////////////////////////////////////////////////////////////////
//
// Core LQ game solver from Basar and Olsder, "Preliminary Notation for
// Corollary 6.1" (pp. 279). All notation matches the text, though we
// shall assume that `c` (additive drift in dynamics) is always `0`, which
// holds because these dynamics are for delta x, delta us.
// Also, we have modified terms slightly to account for linear terms in the
// stage cost for control, i.e.
//       control penalty i = 0.5 \sum_j du_j^T R_ij (du_j + 2 r_ij)
//
// Solve a time-varying, finite horizon LQ game (finds closed-loop Nash
// feedback strategies for both players).
//
// Assumes that dynamics are given by
//           ``` dx_{k+1} = A_k dx_k + \sum_i Bs[i]_k du[i]_k ```
//
// Returns strategies Ps, alphas.
//
///////////////////////////////////////////////////////////////////////////////

#ifndef ILQGAMES_SOLVER_SOLVE_FEEDBACK_LQ_GAME_H
#define ILQGAMES_SOLVER_SOLVE_FEEDBACK_LQ_GAME_H

#include <ilqgames/dynamics/multi_player_integrable_system.h>
#include <ilqgames/solver/lq_solver.h>
#include <ilqgames/utils/linear_dynamics_approximation.h>
#include <ilqgames/utils/quadratic_cost_approximation.h>
#include <ilqgames/utils/strategy.h>

#include <vector>

namespace ilqgames {

class LQFeedbackSolver : LQSolver {
} std::vector<Strategy> SolveFeedbackLQGame(
    const MultiPlayerIntegrableSystem& dynamics,
    const std::vector<LinearDynamicsApproximation>& linearization,
    const std::vector<std::vector<QuadraticCostApproximation>>&
        quadraticization);

}  // namespace ilqgames

#endif