finite_differences_collocation.h

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 *
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 *
 *  Copyright (c) 2020,
 *  TU Dortmund - Institute of Control Theory and Systems Engineering.
 *  All rights reserved.
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 *  Authors: Christoph Rösmann
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#ifndef SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_FINITE_DIFFERENCES_COLLOCATION_H_
#define SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_FINITE_DIFFERENCES_COLLOCATION_H_

#include <corbo-core/factory.h>
#include <corbo-core/time.h>
#include <corbo-core/types.h>
#include <corbo-numerics/dynamics_eval_interface.h>

#ifdef MESSAGE_SUPPORT
#include <corbo-communication/messages/numerics/finite_differences_collocation.pb.h>
#endif

#include <functional>
#include <memory>

namespace corbo {

class FiniteDifferencesCollocationInterface
{
 public:
    using Ptr  = std::shared_ptr<FiniteDifferencesCollocationInterface>;
    using UPtr = std::unique_ptr<FiniteDifferencesCollocationInterface>;

    using StateVector = Eigen::VectorXd;
    using InputVector = Eigen::VectorXd;

    virtual ~FiniteDifferencesCollocationInterface() = default;
    virtual FiniteDifferencesCollocationInterface::Ptr getInstance() const = 0;

    static Factory<FiniteDifferencesCollocationInterface>& getFactory() { return Factory<FiniteDifferencesCollocationInterface>::instance(); }

    virtual void computeEqualityConstraint(const StateVector& x1, const InputVector& u1, const StateVector& x2, double dt,
                                           const SystemDynamicsInterface& system, Eigen::Ref<Eigen::VectorXd> error) = 0;

#ifdef MESSAGE_SUPPORT
    virtual void toMessage(corbo::messages::FiniteDifferencesCollocation& message) const {}
    // Message import
    virtual void fromMessage(const corbo::messages::FiniteDifferencesCollocation& message, std::stringstream* issues = nullptr) {}
#endif
};

using FiniteDifferencesCollocationFactory = Factory<FiniteDifferencesCollocationInterface>;
#define FACTORY_REGISTER_FD_COLLOCATION(type) FACTORY_REGISTER_OBJECT(type, FiniteDifferencesCollocationInterface)

class ForwardDiffCollocation : public FiniteDifferencesCollocationInterface
{
 public:
    // Implements interface method
    FiniteDifferencesCollocationInterface::Ptr getInstance() const override { return std::make_shared<ForwardDiffCollocation>(); }

    // Implements interface method
    void computeEqualityConstraint(const StateVector& x1, const InputVector& u1, const StateVector& x2, double dt,
                                   const SystemDynamicsInterface& system, Eigen::Ref<Eigen::VectorXd> error) override
    {
        assert(error.size() == x1.size());
        // assert(dt > 0 && "dt must be greater then zero!");

        system.dynamics(x1, u1, error);
        error -= (x2 - x1) / dt;
    }

};
FACTORY_REGISTER_FD_COLLOCATION(ForwardDiffCollocation)


class BackwardDiffCollocation : public FiniteDifferencesCollocationInterface
{
 public:
    // Implements interface method
    FiniteDifferencesCollocationInterface::Ptr getInstance() const override { return std::make_shared<BackwardDiffCollocation>(); }

    // Implements interface method
    void computeEqualityConstraint(const StateVector& x1, const InputVector& u1, const StateVector& x2, double dt,
                                   const SystemDynamicsInterface& system, Eigen::Ref<Eigen::VectorXd> error) override
    {
        assert(error.size() == x1.size());
        assert(dt > 0 && "dt must be greater then zero!");

        system.dynamics(x2, u1, error);
        error -= (x2 - x1) / dt;
    }

};
FACTORY_REGISTER_FD_COLLOCATION(BackwardDiffCollocation)


class MidpointDiffCollocation : public FiniteDifferencesCollocationInterface
{
 public:
    // Implements interface method
    FiniteDifferencesCollocationInterface::Ptr getInstance() const override { return std::make_shared<MidpointDiffCollocation>(); }

    // Implements interface method
    void computeEqualityConstraint(const StateVector& x1, const InputVector& u1, const StateVector& x2, double dt,
                                   const SystemDynamicsInterface& system, Eigen::Ref<Eigen::VectorXd> error) override
    {
        assert(error.size() == x1.size());
        assert(dt > 0 && "dt must be greater then zero!");

        system.dynamics(0.5 * (x1 + x2), u1, error);
        error -= (x2 - x1) / dt;
    }

};
FACTORY_REGISTER_FD_COLLOCATION(MidpointDiffCollocation)


class CrankNicolsonDiffCollocation : public FiniteDifferencesCollocationInterface
{
 public:
    // Implements interface method
    FiniteDifferencesCollocationInterface::Ptr getInstance() const override { return std::make_shared<CrankNicolsonDiffCollocation>(); }

    // Implements interface method
    void computeEqualityConstraint(const StateVector& x1, const InputVector& u1, const StateVector& x2, double dt,
                                   const SystemDynamicsInterface& system, Eigen::Ref<Eigen::VectorXd> error) override
    {
        assert(error.size() == x1.size());
        assert(dt > 0 && "dt must be greater then zero!");

        Eigen::VectorXd f1(x1.size());
        system.dynamics(x1, u1, f1);
        system.dynamics(x2, u1, error);
        error = (x2 - x1) / dt - 0.5 * (f1 + error);
    }

};
FACTORY_REGISTER_FD_COLLOCATION(CrankNicolsonDiffCollocation)

}  // namespace corbo

#endif  // SRC_NUMERICS_INCLUDE_CORBO_NUMERICS_FINITE_DIFFERENCES_COLLOCATION_H_