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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The formulation and basic theorems of singularly perturbed nonlinear optimal control problems are discussed and the solution of such problems using matched asymptotic expansions is described.
Two problems are presented in the area of optimal control and its application to the design of attitude control systems for advanced complex aerospace vehicles. The problems discussed are specification of performance criteria in terms of structural load minimization and/or maximum orbital payload injection requirements of the controlled vehicle; and formulation and solution of the optimization problem such that practical control systems are obtained.
The following article describes an optimal control algorithm for the operation and study of an electric microgrid designed to power a lunar habitat. A photovoltaic (PV) generator powers the habitat and the presence of predictable lunar eclipses necessitates a system to prioritize and control loads within the microgrid. The algorithm consists of a reduced order model (ROM) that describes the microgrid, a discretization of the equations that result from the ROM, and an optimization formulation that controls the microgrid’s behavior. In order to validate this approach, the paper presents results from simulation based on lunar eclipse information and a schedule of intended loads.
The Davidon-Broyden class of rank one, quasi-Newton minimization methods is extended from Euclidean spaces to infinite-dimensional, real Hilbert spaces. For several techniques of choosing the step size, conditions are found which assure convergence of the associated iterates to the location of the minimum of a positive definite quadratic functional. For those techniques, convergence is achieved without the problem of the computation of a one-dimensional minimum at each iteration. The application of this class of minimization methods for the direct computation of the solution of an optimal control problem is outlined. The performance of various members of the class are compared by solving a sample optimal control problem. Finally, the sample problem is solved by other known gradient methods, and the results are compared with those obtained with the rank one quasi-Newton methods.
Special purpose rapid computer for providing an on-line solution to the sampled-data time-optimal- control problem in which inputs are subjected to amplitude constraints
The Hybrid Hydraulic-Electric Architecture (HHEA) has, in recent years, been proposed as an energy efficient alternative to conventional load-sensing architectures in mobile machines such as excavators and wheel-loaders. HHEA leverages the advantages of hydraulic power and electric power to eliminate throttling valves while also improving the energy and control performance of the system. The architecture utilizes a set of common pressure rails to provide a majority of power and and a small electric motor driven pump to modulate this power to meet the exact demand. Previous work has developed a computationally efficient Lagrange Multiplier approach for determining the optimal pressure rail selections that minimizes the energy losses in the system. The static model used considers only the energy use for each pressure rail selection but not the losses associated with the valves during the transition. This paper presents an approach to include the switching losses in the model and in the optimization procedure. To capture the switching losses, switching events between different rails and at various input and output flow rates were simulated with consideration of valve spool dynamics. A parameterized model that summarizes the losses is then obtained, allowing switching losses to be added to the previous energy analysis. The performance of the switching loss model was compared with reference data obtained from a high-fidelity simulation model. To incorporate the switching losses into optimal control algorithm, an efficient dynamic programming approach that prevents frequent switching is adopted in place of the Lagrange multiplier approach. The overall effect of switching losses on the energy consumption and optimal control decisions is presented. In general, switching losses contribute to about 9–10% of input energy.
Wiener filtering theory for stationary ergodic inputs with known spectral densities and optimal control transfer functions of random-input nonlinear saturating systems with random unwanted disturbances
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.
This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.
Time optimal control study of second-order linear system with delay
Linear optimal control and least square filtering theory application to control system design of Saturn 5 launch vehicle
Human operators instrument-monitoring behavior noting optimal control, information processing, physical limitations, etc
Optimal control for rocket vehicle in three dimensional central force field
This paper presents the design of a multi-objective optimal controller for the 13.5 aspect ratio Common Research Model (CRM) wind tunnel model. A Pareto front analysis is performed to provide the optimal tradeoff between the competing objectives - gust load alleviation, maneuver load alleviation, and drag minimization - so that the weighting matrices for the control law are selected optimally. Also presented are two formulations of the controller: a state feedback with Kalman filter design, and an output feedback form where sensors are used directly for feedback control. The controller demonstrates a reduced peak-to-peak strain of 45.78% while also reducing drag and mean bending moment. An output feedback formulation for gust load alleviation is formulated and produces a 53% reduction in the strain response due to a gust input.
Here, we study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show that the algorithm exhibits local linear convergence, and that the convergence rate improves exponentially with the overlap size. We also establish global convergence results for a general quadratic programming, which enables the application of the Schwarz scheme inside second-order optimization algorithms (e.g., sequential quadratic programming). The theoretical foundation of our convergence analysis is a sensitivity result of nonlinear OCPs, which we call "exponential decay of sensitivity" (EDS). Intuitively, EDS states that the impact of perturbations at domain boundaries (i.e., initial and terminal time) on the solution decays exponentially as one moves into the domain. Here, we expand a previous analysis available in the literature by showing that EDS holds for both primal and dual solutions of nonlinear OCPs, under uniform second-order sufficient condition, controllability condition, and boundedness condition. We conduct experiments with a quadrotor motion planning problem and a partial differential equations (PDE) control problem to validate our theory, and show that the approach is significantly more efficient than alternating direction method of multipliers and as efficient as the centralized interior-point solver.
This paper considers the l1-optimal control problem for general rational plants. It is shown that, for plants with no poles or zeros on the unit circle, an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs. Exactly or approximately, optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed-loop transfer function. No assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators. It is shown that constrained problems in which a set of outputs is regulated subject to l(infinity)-norm constraints on another set of outputs can be solved using a slight modification of the same algorithm.
Fixed-time regulator problem with time invariant feedback control and unspecified-time regulator problem with bounded control
Road vehicle lane changes often initiate traffic disturbances and can therefore impact road networks’ energy and time efficiency. Furthermore, unexpected changes in traffic conditions may also render lane changes counterproductive for the lane-changing vehicle. Vehicle-to-vehicle connectivity combined with anticipative control could address these challenges via improved lane change decisions by automated vehicles. In a move toward this objective, receding horizon control cast as a mixed-integer quadratic program is used to plan lane changing and acceleration in a coupled optimization. A long-term pacing module, based on Pontryagin’s minimum principle from optimal control theory, sets terminal and input references for receding horizon control to target a user’s expected travel time. To remove nonlinear vehicle dynamics from the receding horizon controller, lane change commands are passed to a pure pursuit steering module whose response is approximated by a second-order linear model. Here, comparison against a rule-based reactive algorithm in arterial and highway scenarios shows an 8.9%–13.7% reduction in energy consumption and a 5.2%–10.3% reduction in the travel time, along with navigational improvements.