We consider the optimal control of feedback linearizable dynamical systems subject to mixed state and constraints. In general, a linearizing does not minimize cost function. Such problems arise frequently in astronautical applications where stringent performance requirements demand optimality over controls. this paper, we pseudospectral (PS) method compute prove that sequence solutions PS-discretized constrained problem converges solution continuous-time under mild numerically verifiable...

Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The of the is based on using differentiation matrix locate switches, kinks, corners, and other discontinuities that typical when solving practical control problems. concept knots Gaussian quadrature rules used generate natural mesh dense near points interest. Several stopping criteria developed new error-estimation formulas Jackson's theorem....

Typical optimal feedback controls are nonsmooth functions. Nonsmooth raise fundamental theoretical problems on the existence and uniqueness of state trajectories. Many these frequently addressed in control applications through concept a Filippov solution. In recent years, simpler π solution has emerged as practical powerful means to address issues. this paper, we advance notion Caratheodory-π- solutions that stem from equivalence between closed-loop recognizing not necessarily closed-form...

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies high-dimensional problems often rely on specific, restrictive problem structures or valid only locally around some nominal trajectory. In this paper, we propose a data-driven method to approximate semiglobal solutions HJB equations general and compute candidate in real-time. To...

J OURNAL OF G UIDANCE , C ONTROL AND D YNAMICS Vol. 30, No. 4, July–August 2007 Low-Thrust, High-Accuracy Trajectory Optimization I. Michael Ross, ∗ Qi Gong, † and Pooya Sekhavat ‡ Naval Postgraduate School, Monterey, California 93943 DOI: 10.2514/1.23181 Multirevolution, very low-thrust trajectory optimization problems have long been considered difficult due to their large time scales high-frequency responses. By relating this difficulty the well-known problem of aliasing in information...

This paper presents a two-time-scale control method to optimize the energy consumption of high-performance-computing data centers through dynamic frequency scaling processors, tasks assignment, and cooling supplement. First, steady dynamical models center are built, which reflect computational interactions thermal relationship among components center. Next, minimization problem for processing parallel task is divided into two parts that correspond model one. Then, solved in manner, i.e.,...

In this paper, we introduce the uncertain optimal control problem of determining a that minimizes expectation an objective functional for system with parameter uncertainty in both dynamics and objective. We present computational framework numerical solution problem, wherein independently drawn random sample is taken from space parameters, approximated by average. The result sequence approximating standard problems can be solved using existing techniques. To analyze performance framework,...

NPSAT1 is a small satellite being built at the Naval Postgraduate School and scheduled to launch in 2007. It primarily employs magnetic sensing actuation for attitude control. The nature of in-house fabrication assembly spacecraft requires reliable computational estimation difficult-to-measure parameters end-product. inherent nonlinear dynamics system makes observer design challenging problem. This paper presents successful implementation unscented Kalman filter (UKF) parameter estimation....

Abstract We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and constraints. In contrast existing results, controller addressed in this paper is allowed be discontinuous. This generalization requires a substantial modification convergence analysis terms both framework as well notion around points discontinuity. Although nonlinear system assumed linearizable, does not necessarily linearize dynamics. Such problems frequently arise astronautical...

A COMMON task for autonomous vehicles is motion planning. Discipline-based design of planning algorithms have led to the development and evolution different techniques solve specific problems. For instance, artificial–potential–function technique [1] a popular method unmanned ground (UGV) robotic manipulators [1–3]. Although this has been used over 30 years, it suffers from possibility vehicle not achieving its goal difficulties in accommodating various environmental constraints [4]. To...

Spacecraft three-axis simulators provide frictionless and, ideally, torque-free hardware simulation platforms that are crucial for validating spacecraft attitude determination and control strategies. To reduce the gravitational torque, distance between simulator center of mass rotation needs to be minimized. This work proposes an automatic balancing system simulators, which uses only three sliding masses during process, without need further actuators. The proposed method is based on adaptive...

Motivated by uncertain parameters in nonlinear dynamic systems, we define a nonclassical optimal control problem where the cost functional is given Riemann–Stieltjes "functional of functional." Using properties sums, minimum principle generated from limit semidiscretization. The minimizes integral Pontryagin Hamiltonian. challenges associated with addressing noncommutative operations integration and minimization are addressed via cubature techniques leading to concept hyper-pseudospectral...

A model predictive control (MPC) method is presented for the optimizing energy consumption of Internet data centers at same time maintaining quality service (QoS). dynamical reflecting computational interactions and thermal relationship between each components center presented. The used to formulate a constrained nonlinear optimal problem minimize both information technology system cooling system. constraints this can capture key design requirements, including QoS device reliability. Solving...

It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show a balancing technique substantially improve optimal control algorithms. We also non-canonical procedures may be used quite effectively to reduce difficulty some hard These results have been successfully for several flight field operations at NASA DoD. A surprising aspect our analysis shows it inadvisable use auto-scaling employed in software packages. The new are...

Based on the improvements of both Genetic Algorithm and Particle Swarm Optimization, a novel IGA-edsPSO(Improved Algorithm-extremum disturbed simple Optimization) Hybrid algorithm is proposed in this paper.An improved performance GA achieved by reducing array space.By discarding particle velocity vector PSO evolutionary equation, sPSO (simple PSO) can avoid problem slow later convergence low precision caused determining maximal factitiously.And edsPSO overstep local extremum point more...

This paper proposes a spacecraft attitude control technique based on the use of center-of-mass shifting. In particular, position vector spacecraft's center pressure with respect to mass is modified by shifting masses, which results in change aerodynamic torque within plane perpendicular drag. an underactuated system. To achieve full three-axis stabilization, additional actuators (either reaction wheel or set magnetic torquers) are considered. An adaptive nonlinear regulation law was designed...

This paper points out that input-to-state stability of zero dynamics having a continuously differentiable (instead locally Lipschitz continuous) gain function suffices to guarantee the existence globally stabilizing, smooth partial-state feedback control laws for cascade systems, without imposing any extra condition. conclusion is proved via small theorem and novel variable separation technique combined with domination design.

In recent years, a large number of nonlinear optimal control problems have been solved by pseudospectral (PS) methods. an effort to better understand the PS approach solving problems, we present convergence results for with mixed state and constraints. A set sufficient conditions are proved under which solution discretized problem converges continuous solution. Conditions duals described illustrated. This leads clarification covector mapping theorem its connections constraint qualifications

Infinite-horizon, nonlinear, optimal, feedback control is one of the fundamental problems in theory. In this paper we propose a solution for problem based on recent progress real-time optimal control. The basic idea to perform implementations through domain transformation technique and Radau pseudospectral method. Two algorithms are considered: free sampling frequency fixed frequency. For both algorithms, theoretical analysis stability closed-loop system provided. Numerical simulations with...

We analyze a few long-standing issues related to the Chebyshev pseudospectral (PS) approximations of nonlinear constrained optimal control problems. The feasibility and consistency PS method are demonstrated. also show that standard primal-dual closure conditions can be mapped primal-only conditions. condition facilitates an easy computation problem covectors which used verify validate computational solution by way continuous-time necessary