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The research carried out in the areas of optimal control and estimation theory and its applications under this grant is reviewed. A listing of the 257 publications that document the research results is presented.
A relatively large amount of computer time was used for the calculation of a optimal trajectory, but it is subject to reduction with moderate effort. The Deterministic, Nonlinear, Optimal Control algorithm yielded excellent aircraft performance in trajectory tracking for the given microburst. It did so by varying the angle of attack to counteract the lift effects of microburst induced airspeed variations. Throttle saturation and aerodynamic stall limits were not a problem for the case considered, proving that the aircraft's performance capabilities were not violated by the given wind field. All closed loop control laws previously considered performed very poorly in comparison, and therefore do not come near to taking full advantage of aircraft performance.
A discrete complementary variational principle is developed and applied to linear and nonlinear discrete-time optimal control systems. Using the variational approach, a primal-dual relationship is established. This relationship provides a precise measure of system suboptimality independent of any a priori knowledge of the optimal solution.
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.
We consider the equilibrium problem for plates with cracks located along rigid inclusions and analyze the dependence of the solution and the derivative of the energy functional on variations of the inclusion size. We establish the solvability of the optimal control problem, where the quality functional is given by the derivative of the energy functional, whereas the control parameter correspond to the inclusion size. A similar analysis is performed for the equilibrium problems for inhomogeneous plates with rigid delaminated inclusions.
Various advanced control sequences for chiller plants with water-side economizers (WSE) have been proposed in literature, but the optimization of those controls is limited. It is possible to maximize energy savings by developing near-optimal control sequences, which are dependent on several factors such as the load profile. To address these gaps, we first identify an advanced control sequence and three key control parameters for chiller plants with WSE. Next, optimizations are performed to minimize energy consumption for seven combinations of control parameters. A chiller plant with WSE system in a warm and marine climate is studied and two load profiles are considered. The system and controls are modeled using the Modelica Buildings library. The results show optimizing the selected control parameters can reduce energy consumption by up to 11% depending on the load profile. Specifically, optimizing the cooling tower efficiency threshold in the condenser water reset control can significantly reduce energy savings for the variable load profile by efficiently shifting the load from the cooling tower to the chiller. This paper provides practical guidance for developing near-optimal control sequences for chiller plant with WSE systems considering impacts such as the load profile.
This paper studies the issue of data-driven optimal control design for traffic signals of oversaturated urban road networks. The signal control system based on the store and forward model is generally uncontrollable for which the controllable decomposition is needed. Instead of identifying the unknown parameters like saturation rates and turning ratios, a finite number of measured trajectories can be used to parametrize the system and help directly construct a transformation matrix for Kalman controllable decomposition through the fundamental lemma of J. C. Willems. On top of that, an infinite-horizon linear quadratic regulator (LQR) problem is formulated considering the constraints of green times for traffic signals. The problem can be solved through a two-phase data-driven learning process, where one solves an infinite-horizon unconstrained LQR problem and the other solves a finite-horizon constrained LQR problem. The simulation result shows the theoretical analysis is effective and the proposed data-driven controller can yield desired performance for reducing traffic congestion.
Linear time varying systems optimal control through decoupling of boundary value problems
We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection, and Acquired Immunodeficiency Syndrome (AIDS) proposed in Silva and Torres (Discr Contin Dyn Syst 35(9):4639–4663, 2015). We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are minimization of the number of HIV-infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.
We establish the unique solvability of the equilibrium problem for a two-layer body. One layer contains a crack, whereas the second one is glued along its edge to the first layer in such a way that to cover one of the crack ends. In the case, where the second layer is a rigid plate, we show that the problem with a rigid patch is the limit of problems with elastic patches as the rigidity parameter tends to infinity. We also study the optimal control problem with the exterior forces acting on both layers taken for the control function.
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.
The control of merging aircraft is formulated as a finite-time, quadratic optimal control problem of a linear system with state and control constraints. The purpose of this paper is to demonstrate that the Hybrid Air Traffic Controller (HAC), which has been previously developed as a solution to this problem, may be easily implemented. Use is made of both the properties of the algebraic solution to the matrix Riccati equation and the structure of the linear model. This approach results in a real-time synthesis procedure for the HAC which does not rely on iterative numerical integration techniques.
Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.
Pontryagin maximum principle to optimize attitude control systems on the basis of minimum fuel or energy consumption
The anthropogenic emission of carbon dioxide (CO{sub 2}) is the prime culprit for the menace of global warming. To achieve the goal of mitigation of global warming, it is crucial to curb the anthropogenic carbon dioxide emissions. The prime anthropogenic source of CO{sub 2} is fossil fuel burning. In this paper, we propose a nonlinear mathematical model to study the impact of technological options, used for the reduction of CO{sub 2} emissions from fossil fuel burning and industrial processes, on the control of atmospheric CO{sub 2}. In the modeling process, it is assumed that the technological options are implemented to curb the CO{sub 2} emissions from the source at a rate proportional to the anthropogenic CO{sub 2} emissions. Model analysis reveals that the atmospheric level of CO{sub 2} can be effectively reduced by increasing the implementation rate of technological options and their efficiency. The strategies which optimally reduce atmospheric CO{sub 2} levels while minimizing the cost associated with the implementation of technological options are identified using optimal control theory. Numerical simulation has been carried out to illustrate theoretical results.
Supercapacitors are gaining wider applications in power systems due to fast dynamic response. Utilizing supercapacitors by means of power electronics interfaces for power compensation is a proven effective technique. For applications such as requency restoration if the cost of supercapacitors maintenance as well as the energy loss on the power electronics interfaces are addressed. It is infeasible to use traditional optimization control methods to mitigate the impacts of frequent cycling. This paper proposes a Front End Controller (FEC) using Generalized Predictive Control featuring real time receding optimization. The optimization constraints are based on cost and thermal management to enhance to the utilization efficiency of supercapacitors. A rigorous mathematical derivation is conducted and test results acquired from Digital Real Time Simulator are provided to demonstrate effectiveness.
A preliminary investigation into the use of modern control theory for the design of controls for a supersonic inlet is described. In particular, the task of controlling a mixed-compression supersonic inlet is formulated as a linear optimal stochastic control and estimation problem. An inlet can exhibit an undesirable instability due to excessive inlet normal shock motion. For the optimal control formulation of the inlet problem, a non quadratic performance index, which is equal to the expected frequency of inlet unstarts, is used. This physically meaningful performance index is minimized for a range of inlet disturbance and measurement noise covariances.
Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics systems. As a test case, we take pulses for single-qudit swap gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be ≲ 0.1 % of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.