A unified approach to optimal control systems with state constraints

Naidu, D. Subbaram; Murillo, Martin J.

doi:10.1109/acc.2003.1242566

Cited by 4 publications

(3 citation statements)

References 8 publications

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“…Linear Quadratic Tracking (LQT) can be applied in order that the system can track the given trajectory r with the minimum performance index J . In this research, LQT is solved by discrete time [2], [5] : Suppose that state equation ()…”

Section: Discrete Linear Quadratic Tracking (Lqt)mentioning

confidence: 99%

Estimation of shoulder and elbow joint angle from linear quadratic tracking based on six muscle force vectors

Herlambang

Rahmalia

Nurhadi

et al. 2022

J. Phys.: Conf. Ser.

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Two dimensional human’s arm is one of the optimal control application. This arm model consists of joint angles consisting of shoulder joint and elbow joint. Beside that, there are also muscle force vectors consisting of pectoralis major, posterior deltoid, brachialis, lateral head of triceps brachii, biceps brachii, and longhead of triceps. Linear Quadratic Tracking (LQT) is constructed to obtain solution of state and optimal control. From state solution and optimal control obtained, they will be used estimation by Backpropagation and ANFIS. From data resulted from LQT simulation, the input used are muscle force vectors. They will be used for estimation the output i.e. angle of shoulder joint and angle of elbow joint. From the LQT simulation, the angle position can follow the given reference function. Then Backpropagation and ANFIS can make estimation in angle of shoulder joint and angle of elbow joint based on six muscle force vectors with small RMSE. In Backpropagation, the estimation result of angle of shoulder joint between target and output with RMSE is 0.0954 and the estimation result of angle elbow joint between target and output with RMSE is 0.2528. In ANFIS, the estimation result of angle of shoulder joint between target and output with RMSE is 0.0062 and the estimation result of angle elbow joint between target and output with RMSE is 0.0526.

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Section: Discrete Linear Quadratic Tracking (Lqt)mentioning

confidence: 99%

Estimation of shoulder and elbow joint angle from linear quadratic tracking based on six muscle force vectors

Herlambang

Rahmalia

Nurhadi

et al. 2022

J. Phys.: Conf. Ser.

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“…e Pe e Qe u Ru e Cx r  Error weighted matrices 0 P  and 0 Q  must be symmetric and positive semidefinite matrices, and control weighted matrix 0 R  must be symmetric and positive definite matrix. The algorithm and computation of LQT in discrete time is as follows (Naidu, 2003) x are given. Kirkpatrick in 1983.…”

Section: Linear Quadratic Tracking (Lqt)mentioning

confidence: 99%

Optimization of Linear Quadratic Tracking (LQT) Weight Matrices Using Simulated Annealing Applied on Planar Arm Model

Rahmalia

Herlambang

Pancahayani

et al. 2020

sjt

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Optimal controls have been applied in this time. One of simple optimal control which will be analyzed in this research is planar arm model dynamic. The planar arm model dynamic consists of joint angles consisting of shoulder joint and elbow joint, angle velocities, and joint torquest due to passive muscle forces. There are control inputs from six muscles in the system. In this research, from planar arm model, it will be designed optimal control using Linear Quadratic Tracking (LQT). The objective function of planar arm model is we will minimimize two angles consisting of shoulder joint and elbow joint. In LQT, the value of performance index depends on the weight matrices so that we should optimize the weight matrices. In this research, the optimization of weight matrices in planar arm model will be applied by Simulated Annealing. The Simulated Annealing method is based on the simulation of thermal annealing of critically heated solids. Based on simulation results, Simulated Annealing can optimize the weight matrices in LQT so that it results optimal performance index with angle as state solution can follow the reference and we also obtain optimal controls from six muscle forces applied.

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“…Subject to the system dynamics of equation 3.1 and with fixed initial and final states, x(t o ) = x o and x(t f ) = x f respectively. In order to solve this OCP Pontryagin's Maximum Principle is used [31]. First compute the Hamiltonian corresponding to the system 3.1:…”

Section: Problem Statementmentioning

confidence: 99%

Nonlinear model predictive control for aggressive maneuvers in a variable pitch quadrotor based on the extended modal series method

Pinzón¹

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A unified approach to optimal control systems with state constraints

Cited by 4 publications

References 8 publications

Estimation of shoulder and elbow joint angle from linear quadratic tracking based on six muscle force vectors

Estimation of shoulder and elbow joint angle from linear quadratic tracking based on six muscle force vectors

Optimization of Linear Quadratic Tracking (LQT) Weight Matrices Using Simulated Annealing Applied on Planar Arm Model

Nonlinear model predictive control for aggressive maneuvers in a variable pitch quadrotor based on the extended modal series method

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