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Control-theory design package, called Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), aids in design of controllers and optimal filters for systems modeled by linear, time invariant differential and difference equations. ORACLS is particularly attractive rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete forms.
Optimal linear control theory to develop quadratic cost-criterion control law for flexible rocket vehicle
This paper presents implementation of two control policies on SCOLE (Space Control Laboratory Experiment), a laboratory apparatus representing an offset-feed antenna attached to the Space Shuttle by a flexible mast. In the first case, the flexible mast was restrained by cables, permitting modeling of SCOLE as a rigid-body. Starting from an arbitrary state, SCOLE was maneuvered to a specified terminal state using rigid-body minimum-time control law. In the second case, the so called single step optimal control (SSOC) theory is applied to suppress vibrations of the flexible mast mounted as a cantilever beam. Based on the SSOC theory, two parameter optimization algorithms were developed.
The man machine interface between the human driver and his automobile during car following tasks was examined. A direct connection between models of the human operator and the theory of optimal control was established for car following situations involving both linear and nonlinear car dynamics. Results obtained from several types of mathematical models are discussed. Conventional parameter identification techniques were used to obtain the parameters of these models by comparing their performance to data obtained by aerial photogrammetry. The results indicate that there are two general classes of model structures: models assumed to have preview information and models without preview.
This paper presents a control theoretic approach to modeling human response errors (HRE) in the flight simulation domain. The human pilot is modeled as a supervisor of a highly automated system. The synthesis uses the theory of optimal control pilot modeling for integrating the pilot's observation error and the error due to the simulation model (experimental error). Methods for solving the HRE problem are suggested. Experimental verification of the models will be tested in a flight quality handling simulation.
The control design problem for the class of future spacecraft referred to as large space structures (LSS) is by now well known. The issue is the reduced order control of a very high order, lightly damped system with uncertain system parameters, particularly in the high frequency modes. A design methodology which incorporates robustness considerations as part of the design process is presented. Combining pertinent results from multivariable systems theory and optimal control and estimation, LQG eigenstructure assignment and LQG frequency shaping, were used to improve singular value robustness measures in the presence of control and observation spillover.
A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.
Given the predicted growth in air transportation, the potential exists for significant market niches for rotary wing subsonic vehicles. Technological advances which optimise rotorcraft aeromechanical behaviour can contribute significantly to both their commercial and military development, acceptance, and sales. Examples of the optimisation of rotorcraft aeromechanical behaviour which are of interest include the minimisation of vibration and/or loads. The reduction of rotorcraft vibration and loads is an important means to extend the useful life of the vehicle and to improve its ride quality. Although vibration reduction can be accomplished by using passive dampers and/or tuned masses, active closed-loop control has the potential to reduce vibration and loads throughout a.wider flight regime whilst requiring less additional weight to the aircraft man that obtained by using passive methads. It is ernphasised that the analysis described herein is applicable to all those rotorcraft aeromechanical behaviour optimisation problems for which the relationship between the harmonic control vector and the measurement vector can be adequately described by a neural-network model.
Use of imbedding theory to construct autonomous optimal control problems with free termination time
The rapid growth in the number of devices and their connectivity has enlarged the attack surface and made cyber systems more vulnerable. As attackers become increasingly sophisticated and resourceful, mere reliance on traditional cyber protection, such as intrusion detection, firewalls, and encryption, is insufficient to secure the cyber systems. Cyber resilience provides a new security paradigm that complements inadequate protection with resilience mechanisms. A Cyber-Resilient Mechanism (CRM) adapts to the known or zero-day threats and uncertainties in real-time and strategically responds to them to maintain the critical functions of the cyber systems in the event of successful attacks. Feedback architectures play a pivotal role in enabling the online sensing, reasoning, and actuation process of the CRM. Reinforcement Learning (RL) is an important gathering of algorithms that epitomize the feedback architectures for cyber resilience. It allows the CRM to provide dynamic and sequential responses to attacks with limited or without prior knowledge of the environment and the attacker. In this work, we review the literature on RL for cyber resilience and discuss the cyber-resilient defenses against three major types of vulnerabilities, i.e., posture-related, information-related, and human-related vulnerabilities. Here we introduce moving target defense, defensive cyber deception, and assistive human security technologies as three application domains of CRMs to elaborate on their designs. The RL algorithms also have vulnerabilities themselves. We explain the major vulnerabilities of RL and present develop several attack models where the attacker target the information exchanged between the environment and the agent: the rewards, the state observations, and the action commands. We show that the attacker can trick the RL agent into learning a nefarious policy with minimum attacking effort. The paper introduces several defense methods to secure the RL-enabled systems from these attacks. However, there is still a lack of works that focuses on the defensive mechanisms for RL-enabled systems. Last but not least, we discuss the future challenges of RL for cyber security and resilience and emerging applications of RL-based CRMs.
We present differentiable predictive control (DPC), a method for offline learning of constrained neural control policies for nonlinear dynamical systems with performance guarantees. We show that the sensitivities of the parametric optimal control problem can be used to obtain direct policy gradients. Specifically, we employ automatic differentiation (AD) to efficiently compute the sensitivities of the model predictive control (MPC) objective function and constraints penalties. To guarantee safety upon deployment, we derive probabilistic guarantees on closed-loop stability and constraint satisfaction based on indicator functions and Hoeffding’s inequality. We empirically demonstrate that the proposed method can learn neural control policies for various parametric optimal control tasks. In particular, we show that the proposed DPC method can stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. Our DPC method has practical time savings compared to alternative approaches for fast and memory-efficient controller design. Specifically, DPC does not depend on a supervisory controller as opposed to approximate MPC based on imitation learning. We demonstrate that, without losing performance, DPC is scalable with greatly reduced demands on memory and computation compared to implicit and explicit MPC while being more sample efficient than model-free reinforcement learning (RL) algorithms.
Matrix Riccati equations for optimization in control theory
Optimal lateral guidance switching thresholds for low L/D shuttle vehicle entry, using optimal stochastic control theory for problem formulation in conjunction with dynamic programming
Linear optimal quadratic control theory is applied to a low wing-loading STOL aircraft for ride quality and flight path following. Design criteria include minimum rms response to wind turbulence and desired transient response characteristics. Design techniques include proper choosing of design versus evaluation models, choosing appropriate performance index responses, and use of classical evaluation techniques. Results are obtained through a combination of frequency response shaping and gust observation. Effects of control rate and authority saturation are examined with a new rapid calculation of random input describing functions. Parameter sensitivity is also evaluated using a Liapunov type matrix equation.
Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.
The underlying motivation and concepts are presented, along with a review of the development and application of the model. The structure of the model is described and results validating the model are presented.
In this paper, step-by-step procedures of applying the H-infinity theory to robust control systems design are given. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H-infinity control theory and to clear up some misconceptions about H-infinity theory like high-gain controller and numerical obstacles, etc. An efficient algorithm is used to compute the optimal H-infinity norm. The Glover and Doyle (1988) controller formulas are slightly modified and used to construct an optimal controller without any numerical difficulties.
After a short recall concerning the aeroelastic equations, active control law based on optimal stochastic control theory is synthesized for a wing flutter and gust response. Robustness of the control system due to structured and unstructured uncertainties is considered. Robustness recovery technique is applied to improve the stability margin.