Primal or Dual Terminal Constraints in Economic MPC? Comparison and Insights

A new design method for trajectory shaping guidance laws with the impact angle constraint is proposed in this study. The basic idea is that the multiplier introduced to combine the equations for the terminal constraints is used to shape a flight trajectory as desired. To this end, the general form of impact angle control guidance (IACG) is first derived as a function of an arbitrary constraint-combining multiplier using the optimal control. We reveal that the constraint-combining multiplier satisfying the kinematics can be expressed as a function of state variables. From this result, the constraint-combining multiplier to achieve a desired trajectory can be obtained. Accordingly, when the desired trajectory is designed to satisfy the terminal constraints, the proposed method directly can provide a closed form of IACG laws that can achieve the desired trajectory. The potential significance of the proposed result is that various trajectory shaping IACG laws that can cope with various guidance goals can be readily determined compared to existing approaches. In this study, several examples are shown to validate the proposed method. The results also indicate that previous IACG laws belong to the subset of the proposed result. Finally, the characteristics of the proposed guidance laws are analyzed through numerical simulations.

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Complexity minimisation of suboptimal MPC without terminal constraints

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.1682 ◽

2020 ◽

Vol 53 (2) ◽

pp. 6089-6094

Author(s):

Andrei Pavlov ◽

Matthias Müller ◽

Chris Manzie ◽

Iman Shames

Keyword(s):

Terminal Constraints

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A new neuro-based solution for closed-loop optimal guidance with terminal constraints

10.2514/6.1999-4068 ◽

1999 ◽

Cited By ~ 1

Author(s):

N. Rahbar ◽

M. Bahrami ◽

M. Menhaj

Keyword(s):

Closed Loop ◽

Optimal Guidance ◽

Terminal Constraints

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3D Nonlinear Guidance Law for Bank-to-Turn Missile

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.317-319.727 ◽

2011 ◽

Vol 317-319 ◽

pp. 727-733

Author(s):

Shuang Chun Peng ◽

Liang Pan ◽

Tian Jiang Hu ◽

Lin Cheng Shen

Keyword(s):

Three Dimensional ◽

Lyapunov Theory ◽

Line Of Sight ◽

Rate Model ◽

Guidance Law ◽

Terminal Constraints ◽

Guidance Laws ◽

3D Guidance ◽

Guidance Model ◽

Vector Description

A new three-dimensional (3D) nonlinear guidance law is proposed and developed for bank-to-turn (BTT) with motion coupling. First of all, the 3D guidance model is established. In detail, the line-of-sight (LOS) rate model is established with the vector description method, and the kinematics model is divided into three terms of pitching, swerving and coupling, then by using the twist-based method, the LOS direction changing model is built for designing the guidance law with terminal angular constraints. Secondly, the 3D guidance laws are designed with Lyapunov theory, corresponding to no terminal constraints and terminal constraints, respectively. And finally, the simulation results show that the proposed guidance law can effectively satisfy the guidance precision requirements of BTT missile.

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New method for Handling of Infrastructural Constraints for Integrated Modeling in Steady Case

10.2118/206542-ms ◽

2021 ◽

Author(s):

Dmitry Moiseevich Olenchikov

Keyword(s):

Optimal Solution ◽

Field Development ◽

Flow Models ◽

Second Stage ◽

Operation Modes ◽

Reservoir Flow ◽

Terminal Constraints ◽

Surface Network ◽

Two Stages ◽

And Control

Abstract Recently, more and more reservoir flow models are being extended to integrated ones to consider the influence of the surface network on the field development. A serious numerical problem is the handling of constraints in the form of inequalities. It is especially difficult in combination with optimization and automatic control of well and surface equipment. Traditional numerical methods solve the problem iteratively, choosing the operation modes for network elements. Sometimes solution may violate constraints or not be an optimal. The paper proposes a new flexible and relatively efficient method that allows to reliably handle constraints. The idea is to work with entire set of all possible operation modes according to constraints and control capabilities. Let's call this set an operation modes domain (OMD). The problem is solved in two stages. On the first stage (direct course) the OMD are calculated for all network elements from wells to terminal. Constraints are handled by narrowing the OMD. On the second stage (backward course) the optimal solution is chosen from OMD.

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Minimum Energy Control of a Unicycle Model Robot

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4050845 ◽

2021 ◽

Author(s):

Youngjin Kim ◽

Tarunraj Singh

Keyword(s):

Optimal Control ◽

Minimum Energy ◽

Kinematic Model ◽

Elliptic Functions ◽

Terminal Point ◽

Jacobi Elliptic Functions ◽

Differential Drive ◽

Terminal Constraints ◽

Differential Drive Robot ◽

Point To Point

Abstract Point-to-point path planning for a kinematic model of a differential-drive wheeled mobile robot (WMR) with the goal of minimizing input energy is the focus of this work. An optimal control problem is formulated to determine the necessary conditions for optimality and the resulting two point boundary value problem is solved in closed form using Jacobi elliptic functions. The resulting nonlinear programming problem is solved for two variables and the results are compared to the traditional shooting method to illustrate that the Jacobi elliptic functions parameterize the exact profile of the optimal trajectory. A set of terminal constraints which lie on a circle in the first quadrant are used to generate a set of optimal solutions. It is noted that for maneuvers where the angle of the vector connecting the initial and terminal point is greater than a threshold, which is a function of the radius of the terminal constraint circle, the robot initially moves into the third quadrant before terminating in the first quadrant. The minimum energy solution is compared to two other optimal control formulations: (1) an extension of the Dubins vehicle model where the constant linear velocity of the robot is optimized for and (2) a simple turn and move solution, both of whose optimal paths lie entirely in the first quadrant. Experimental results are used to validate the optimal trajectories of the differential-drive robot.

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