On the removal of ill conditioning effects in the computation of optimal controls

Ill conditioning effects eliminated in nonlinear programming algorithms for optimal control

A survey of methods of feasible directions for the solution of optimal control problems

Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category

Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861

A modified secant method for unconstrained minimization

A gradient-secant algorithm for unconstrained optimization problems is presented. The algorithm uses Armijo gradient method iterations until it reaches a region where the Newton method is more efficient, and then switches over to a secant form of operation. It is concluded that an efficient method for unconstrained minimization has been developed, and that any convergent minimization method can be substituted for the Armijo gradient method

Constrained Minimization Under Vector-Valued Criteria in Linear Topological Spaces

Constrained minimization under vector valued criteria in linear topological space

Computational experiments in the optimal slewing of flexible structures

Numerical experiments on the problem of moving a flexible beam are discussed. An optimal control problem is formulated and transcribed into a form which can be solved using semi-infinite optimization techniques. All experiments were carried out on a SUN 3 microcomputer

Second order conditions of optimality for constrained optimization problems in finite dimensional spaces

Conditions of optimality for constrained optimization proble

Advanced theoretical and experimental studies in automatic control and information systems

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included

Decision-making for unmanned aerial vehicle operation in icing conditions

With the increased use of unmanned aerial systems (UAS) for civil and commercial applications, there is a strong demand for new regulations and technology that will eventually permit for the integration of UAS in unsegregated airspace. This requires new technology to ensure sufficient safety and a smooth integration process. The absence of a pilot on board a vehicle introduces new problems that do not arise in manned flight. One challenging and safety-critical issue is flight in known icing conditions. Whereas in manned flight, dealing with icing is left to the pilot and his appraisal of the situation at hand; in unmanned flight, this is no longer an option and new solutions are required. To address this, an icing-related decision-making system (IRDMS) is proposed. The system quantifies in-flight icing based on changes in aircraft performance and measurements of environmental properties, and evaluates what the effects on the aircraft are. Based on this, it determines whether the aircraft can proceed, and whether and which available icing protection systems should be activated. In this way, advice on an appropriate response is given to the operator on the ground, to ensure safe continuation of the flight and avoid possible accidents