Transition to nonlinear ℋ/sub ∞/ optimal control from inverse-optimal solution for Euler-Lagrange system

2002 ◽  
Author(s):  
Jonghoon Park ◽  
Wan Kyun Chung
Keyword(s):  
Optimal Control ◽  
Optimal Solution ◽  
Lagrange System

scholarly journals Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

2020 ◽  
Vol 18 (1) ◽  
pp. 1302-1316
Author(s):  
Guobing Fan ◽  
Zhifeng Yang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Weak Solution ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Dispersive Equation ◽  
Weak Dissipation ◽  
Formula Type

Abstract In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

Solving multiobjective optimal control problems using an improved scalarization method

2020 ◽  
Vol 37 (4) ◽  
pp. 1524-1547
Author(s):  
Gholam Hosein Askarirobati ◽  
Akbar Hashemi Borzabadi ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Uniform Distribution ◽  
Optimal Control Problems ◽  
Pareto Frontier ◽  
Optimal Solution ◽  
Control Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Optimal Control

Abstract Detecting the Pareto optimal points on the Pareto frontier is one of the most important topics in multiobjective optimal control problems (MOCPs). This paper presents a scalarization technique to construct an approximate Pareto frontier of MOCPs, using an improved normal boundary intersection (NBI) scalarization strategy. For this purpose, MOCP is first discretized and then using a grid of weights, a sequence of single objective optimal control problems is solved to achieve a uniform distribution of Pareto optimal solutions on the Pareto frontier. The aim is to achieve a more even distribution of Pareto optimal solutions on the Pareto frontier and improve the efficiency of the algorithm. It is shown that in contrast to the NBI method, where Pareto optimality of solutions is not guaranteed, the obtained optimal solution of the scalarized problem is a Pareto optimal solution of the MOCP. Finally, the ability of the proposed method is evaluated and compared with other approaches using several practical MOCPs. The numerical results indicate that the proposed method is more efficient and provides more uniform distribution of solutions on the Pareto frontier than the other methods, such a weighted sum, normalized normal constraint and NBI.

scholarly journals State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Qingyi Zhu ◽  
Seng W. Loke ◽  
Ye Zhang
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Computer Virus ◽  
Numerical Results ◽  
Difference Approximation ◽  
External Device ◽  
Virus Propagation ◽  
The Impact

The rapid propagation of computer virus is one of the greatest threats to current cybersecurity. This work deals with the optimal control problem of virus propagation among computers and external devices. To formulate this problem, two control strategies are introduced: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers. Then the combination of both the impact of infection and the cost of controls is minimized. In contrast with previous works, this paper takes into account a state-based cost weight index in the objection function instead of a fixed one. By using Pontryagin’s minimum principle and a modified forward-backward difference approximation algorithm, the optimal solution of the system is investigated and numerically solved. Then numerical results show the flexibility of proposed approach compared to the regular optimal control. More numerical results are also given to evaluate the performance of our approach with respect to various weight indexes.

scholarly journals On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yeşim Saraç ◽  
Murat Subaşı
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Iterative Procedure ◽  
Control Function ◽  
Optimal Solution ◽  
Test Problems ◽  
Initial Condition ◽  
Final Time ◽  
State Variable ◽  
Suitable Norm

We use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the existence and the uniqueness of the optimal solution and establish the optimality condition. An iterative algorithm is constructed to compute the required optimal control as limit of a suitable subsequence of controls. An iterative procedure is implemented and used to numerically solve some test problems.

Robust Nonlinear Optimal Solution to the Lunar Landing Guidance by Using Neighboring Optimal Control

2011 ◽  
Vol 24 (1) ◽  
pp. 20-30 ◽  
Author(s):  
Hamed Hossein Afshari ◽  
Jafar Roshanian ◽  
Alireza Novinzadeh
Keyword(s):  
Optimal Control ◽  
Optimal Solution ◽  
Lunar Landing ◽  
Neighboring Optimal Control

scholarly journals Optimal controllability for scalar conservation laws with convex flux

2014 ◽  
Vol 11 (03) ◽  
pp. 477-491 ◽  
Author(s):  
Adimurthi ◽  
Shyam Sundar Ghoshal ◽  
G. D. Veerappa Gowda
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conservation Laws ◽  
Linear Problem ◽  
Optimal Solution ◽  
Scalar Conservation Laws ◽  
Existence Of A Solution ◽  
New Strategy ◽  
Scalar Conservation

The optimal control problem for Burgers equation was first considered by Castro, Palacios and Zuazua. They proved the existence of a solution and proposed a numerical scheme to capture an optimal solution via the method of "alternate decent direction". In this paper, we introduce a new strategy for the optimal control problem for scalar conservation laws with convex flux. We propose a new cost function and by the Lax–Oleinik explicit formula for entropy solutions, the nonlinear problem is converted to a linear problem. Exploiting this property, we prove the existence of an optimal solution and, by a backward construction, we give an algorithm to capture an optimal solution.

scholarly journals Economic Order Quality Model for Determining the Sales Prices of Fresh Goods at Various Points in Time

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Po-Yu Chen
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Food Products ◽  
Economic Order ◽  
Quality Model ◽  
Sales Price ◽  
Lack Of Information

Although the safe consumption of goods such as food products, medicine, and vaccines is related to their freshness, consumers frequently understand less than suppliers about the freshness of goods when they purchase them. Because of this lack of information, apart from sales prices, consumers refer only to the manufacturing and expiration dates when deciding whether to purchase and how many of these goods to buy. If dealers could determine the sales price at each point in time and customers’ intention to buy goods of varying freshness, then dealers could set an optimal inventory cycle and allocate a weekly sales price for each point in time, thereby maximizing the profit per unit time. Therefore, in this study, an economic order quality model was established to enable discussion of the optimal control of sales prices. The technique for identifying the optimal solution for the model was determined, the characteristics of the optimal solution were demonstrated, and the implications of the solution’s sensitivity analysis were explained.

scholarly journals The Expected Total Cost Criterion for Markov Decision Processes under Constraints: A Convex Analytic Approach

2012 ◽  
Vol 44 (3) ◽  
pp. 774-793 ◽  
Author(s):  
François Dufour ◽  
M. Horiguchi ◽  
A. B. Piunovskiy
Keyword(s):  
Optimal Control ◽  
Markov Decision Processes ◽  
Optimal Solution ◽  
Decision Processes ◽  
Linear Program ◽  
Occupation Measure ◽  
Stationary Policy ◽  
Total Cost ◽  
Markov Decision ◽  
Expected Total Cost

This paper deals with discrete-time Markov decision processes (MDPs) under constraints where all the objectives have the same form of expected total cost over the infinite time horizon. The existence of an optimal control policy is discussed by using the convex analytic approach. We work under the assumptions that the state and action spaces are general Borel spaces, and that the model is nonnegative, semicontinuous, and there exists an admissible solution with finite cost for the associated linear program. It is worth noting that, in contrast to the classical results in the literature, our hypotheses do not require the MDP to be transient or absorbing. Our first result ensures the existence of an optimal solution to the linear program given by an occupation measure of the process generated by a randomized stationary policy. Moreover, it is shown that this randomized stationary policy provides an optimal solution to this Markov control problem. As a consequence, these results imply that the set of randomized stationary policies is a sufficient set for this optimal control problem. Finally, our last main result states that all optimal solutions of the linear program coincide on a special set with an optimal occupation measure generated by a randomized stationary policy. Several examples are presented to illustrate some theoretical issues and the possible applications of the results developed in the paper.

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