Stochastic measures of performance robustness in aircraft control systems
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Ray, Laura R.↗
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Investigation of optimization of attitude control systems Quarterly progress report, 1 Jan. - 31 Mar. 1966
Space vehicle, stochastic process, and bounded phase-coordinate process optimal control problems in attitude control system optimization study
ATTITUDE CONTROL↗
Linear regulator design for stochastic systems by a multiple time-scales method
This short paper develops a hierarchically structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short-period modes of the longitudinal dynamics of the F-8 aircraft.
Teneketzis, D.↗
A Unifying View of Estimation and Control Using Belief Propagation With Application to Path Planning
The use of estimation techniques on stochastic models to solve control problems is an emerging paradigm that falls under the rubric of Active Inference (AI) and Control as Inference (CAI). In this work, we use probability propagation on factor graphs to show that various algorithms proposed in the literature can be seen as specific composition rules in a factor graph. We show how this unified approach, presented both in probability space and in log of the probability space, provides a very general framework that includes the Sum-product, the Max-product, Dynamic programming and mixed Reward/Entropy criteria-based algorithms. The framework also expands algorithmic design options that lead to new smoother or sharper policy distributions. We propose original recursions such as: a generalized Sum/Max-product algorithm, a Smooth Dynamic programming algorithm and a modified versions of the Reward/Entropy algorithm. The discussion is carried over with reference to a path planning problem where the recursions that arise from various cost functions, although they may appear similar in scope, bear noticeable differences. We provide a comprehensive table of composition rules and a comparison through simulations, first on a synthetic small grid with a single goal with obstacles, and then on a grid extrapolated from a real-world scene with multiple goals and a semantic map.
Francesco A. N. Palmieri↗
A linear stochastic model of the human operator
A linear stochastic model of the human operator is developed and applied to the problem of piloted control of an aircraft. The pilot and aircraft are modeled as linear time-invariant systems containing both process and measurement noise. The loop closure by the pilot is determined by formulating the problem as an optimal stochastic control problem. The solution to the optimal control problem yields not only the pilot's optimal control output which he uses to control the vehicle, but also the optimal combination of his observations of the vehicle states upon which the pilot bases his control. A method is presented so that, using experimental pilot vehicle data, the cost functional which is minimized in the optimal control problem will be numerically equal to the pilot rating that the pilot would associate with the given vehicle and task.
Durrett, J. C.↗
Knowledge-based processing for aircraft flight control
This Contractor Report documents research in Intelligent Control using knowledge-based processing in a manner dual to methods found in the classic stochastic decision, estimation, and control discipline. Such knowledge-based control has also been called Declarative, and Hybid. Software architectures were sought, employing the parallelism inherent in modern object-oriented modeling and programming. The viewpoint adopted was that Intelligent Control employs a class of domain-specific software architectures having features common over a broad variety of implementations, such as management of aircraft flight, power distribution, etc. As much attention was paid to software engineering issues as to artificial intelligence and control issues. This research considered that particular processing methods from the stochastic and knowledge-based worlds are duals, that is, similar in a broad context. They provide architectural design concepts which serve as bridges between the disparate disciplines of decision, estimation, control, and artificial intelligence. This research was applied to the control of a subsonic transport aircraft in the airport terminal area.
Painter, John H.↗
Chance-Constrained Guidance With Non-Convex Constraints
Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.
FROM↗
Efficient Probabilistic Computing with Stochastic Perovskite Nickelates
Probabilistic computing has emerged as a viable approach to solve hard optimization problems. Devices with inherent stochasticity can greatly simplify their implementation in electronic hardware. In this report we demonstrate intrinsic stochastic resistance switching controlled via electric fields in perovskite nickelates doped with hydrogen. The ability of hydrogen ions to reside in various metastable configurations in the lattice leads to a distribution of transport gaps. With experimentally characterized p-bits, a shared-synapse p-bit architecture demonstrates highly parallelized and energy-efficient solutions to optimization problems such as integer factorization and Boolean satisfiability. The results introduce perovskite nickelates as scalable potential candidates for probabilistic computing and showcase the potential of light-element dopants in next-generation correlated semiconductors.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors
This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Differential geometric methods in system theory.
Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.
Brockett, R. W.↗
The effects of stability augmentation on the gust response of a STOL aircraft during a curved manual approach
The task of investigating the effect of SAS was formulated as two optimal control problems for stochastic systems: (1) to compute SAS gains with a rate model in the performance index algorithm; and (2) to calculate the pilot gains and system gust response using an optimal pilot model. Both problems were solved to yield reasonable low gains for the pilot and SAS, and the lateral directional mode poles and the longitudinal short period poles could be placed accurately by the model matching algorithm. Of the longitudinal (SAS) poles achieved, the vertical rms path error was least for the unaugmented poles. The lateral rms path error was an order of magnitude larger than the vertical error and showed a plus or minus 50 percent variation with SAS. It increased with dutch roll frequency and damping, and it decreased most significantly with increased roll stability. The variation in lateral error with bank angle for curved flight was also a significant function of the augmented poles.
Porter, M. B., Jr.↗
Comparison of Acoustic Models and Trajectory Generation Methods for an Acoustically-Aware Aircraft
This paper presents a comparison of trajectory generation methodologies using acoustic source noise models of different fidelity for motion planning for an acoustically-aware aircraft subject to constraints on the vehicle dynamic performance, mission, and acoustic footprint of the vehicle at a set of (three-dimensional) observer locations. The performance of a pre-mission Bézier curve-based planner and a (near) real-time stochastic model predictive control planner are compared. Additionally, a comparison is made between the motion planning performance using a lower-fidelity acoustic model based on propeller tip Mach number and omni-directional sound power radiation, and a hemisphere-based higher-fidelity acoustic model. It is demonstrated that the asymmetry in hemisphere-based acoustic model can be exploited for improved flight path planning and trajectory-tracking performance in the presence of acoustic constraints.
Kasey A Ackerman↗
Information distribution in distributed microprocessor based flight control systems
This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.
Montgomery, R. C.↗
Nonlinear power flow control for networked AC/DC microgrids
A method for designing feedforward and feedback controllers for integration of stochastic sources and loads into a nonlinear networked AC/DC microgrid system is provided. A reduced order model for general networked AC/DC microgrid systems is suitable for HSSPFC control design. A simple feedforward steady state solution is utilized for the feedforward controls block. Feedback control laws are provided for the energy storage systems. A HSSPFC controller design is implemented that incorporates energy storage systems that provides static and dynamic stability conditions for both the DC random stochastic input side and the AC random stochastic load side. Transient performance was investigated for the feedforward/feedback control case. Numerical simulations were performed and provided power and energy storage profile requirements for the networked AC/DC microgrid system overall performance. The HSSPFC design can be implemented in the Matlab/Simulink environment that is compatible with real time simulation/controllers.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion
In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.
Maldonado, BryanP. [Oak Ridge National Lab. (ORNL)↗
Studies of thrust vector control of large space vehicles Final report
Display systems, fluid amplification techniques, stochastic processes, and thrust vector control systems
Boland, J. S., III↗
Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs
The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.
Hyland, D. C.↗
Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes
The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.
Herencia-Zapana, Heber↗