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This paper presents a primal–dual interior-point (pdip) optimization algorithm for solving extreme-scale model predictive control (mpc) problems with linear dynamics, polytopic constraints, and quadratic/linear costs which are all invariant under the symmetric-group. We show that exploiting symmetry can reduce the computational and memory burden of extreme-scale or fast-paced applications of mpc. Our algorithm transforms the original inputs, states, and constraints of the mpc problem into a symmetric domain. The premise of our algorithm is that the numerical linear algebra used to solve the optimization problem has lower computational and memory complexity in the transformed domain. We demonstrate our algorithm for a heating, ventilation, and air-conditioning (hvac) numerical example. We show that, for our largest hvac control problem, our symmetry exploiting the pdip algorithm reduces the computation-time from minutes to seconds in comparison with the baseline pdip algorithm. Furthermore, we show that the presented symmetry exploiting pdip algorithm outperforms a state-of-the-art symmetry exploiting optimization algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The control algorithm hierarchy of motion control for over-actuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a high-level motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet the overall motion control objectives. Second, a control allocation algorithm coordinates the different effectors such that they together produce the desired virtual control efforts, if possible. Third, low-level control algorithms may be used to control each individual effector via its actuators. Control allocation offers the advantage of a modular design where the high-level motion control algorithm can be designed without detailed knowledge about the effectors and actuators. Important issues such as input saturation and rate constraints, actuator and effector fault tolerance, and meeting secondary objectives such as power efficiency and tear-and-wear minimization are handled within the control allocation algorithm. The objective of the present paper is to survey control allocation algorithms, motivated by the rapidly growing range of applications that have expanded from the aerospace and maritime industries, where control allocation has its roots, to automotive, mechatronics, and other industries. The survey classifies the different algorithms according to two main classes based on the use of linear or nonlinear models, respectively. The presence of physical constraints (e.g input saturation and rate constraints), operational constraints and secondary objectives makes optimization-based design a powerful approach. The simplest formulations allow explicit solutions to be computed using numerical linear algebra in combination with some logic and engineering solutions, while the more challenging formulations with nonlinear models or complex constraints and objectives call for iterative numerical optimization procedures. Experiences using the different methods in aerospace, maritime, automotive and other application areas are discussed. The paper ends with some perspectives on new applications and theoretical challenges. [Copyright &y& Elsevier]

Abstract: Skid-steered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously during a maneuver as well as introduces complications to the observation of the vehicle’s state, both of which affect a controller’s performance. This paper addresses estimation of contact state by applying switched system optimization to estimate skidding properties of the skid-steered vehicle. In order to treat the skid-steered vehicle as a switched system, the vehicle’s ground interaction is modeled using Coulomb friction, thereby partitioning the system dynamics into four distinct modes, one for each combination of the forward and back wheel pairs sticking or skidding. Thus, as the vehicle maneuvers, the system propagates over some mode sequence, transitioning between modes over some set of switching times. This paper presents second-order optimization algorithms for estimating these switching times. We emphasize the importance of the second-order algorithm because it exhibits quadratic convergence and because even for relatively simple examples, first-order methods fail to converge on time scales compatible with real-time operation. Furthermore, the paper presents a technique for estimating the mode sequence by optimizing a relaxation of the switched system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an optimization-based adaptive Kalman filtering method is proposed. The method produces an estimate of the process noise covariance matrix by solving an optimization problem over a short window of data. The algorithm recovers the observations from a system without a priori knowledge of system dynamics. Potential applications include target tracking using a network of nonlinear sensors, servoing, mapping, and localization. The algorithm is demonstrated in simulations on a tracking example for a target with coupled and nonlinear kinematics. Simulations indicate superiority over a standard MMAE algorithm for a large class of systems. [Copyright &y& Elsevier]

Abstract: A novel approach based on probability and randomization has emerged to synergize with the standard deterministic methods for control of systems with uncertainty. The main objective of this paper is to provide a broad perspective on this area of research known as “probabilistic robust control”, and to address in a systematic manner recent advances. The focal point is on design methods, based on the interplay between uncertainty randomization and convex optimization, and on the illustration of specific control applications. [Copyright &y& Elsevier]

Abstract: Holonic manufacturing systems (HMS) is based on the notion of holon, an autonomous, cooperative and intelligent entity to provide a econfigurable, flexible and decentralized manufacturing environment to respond to changing needs and opportunities. A set of holons that cooperate to achieve a goal forms a holarchy. How to design a mechanism to form a holarchy to achieve a goal while minimizing the overall cost is a challenge. The objectives of this paper are to propose models and develop collaborative algorithms to guide the holons to form a holarchy to coherently move toward the desired goal state ultimately. We adopt contract net protocol (CNP) to model mutual selection of holons in forming a holarchy. We formulate a holarchy optimization problem to minimize the cost subject to the feasibility constraints. To analyze the feasibility of a holarchy, a Petri net (PN) model is proposed. As classical PN models do not take into account the cost involved in firing transitions, we augment the PN model with cost functions in the problem formulation. Due to the distributed architecture of HMS, the internal structure of each potential holarchy that acts as bidder in CNP is not available to the manager. A key issue is to determine the feasibility of a holarchy without constructing the whole PN model of the given hierarchy. We study the feasible conditions for a holarchy and propose a collaborative algorithm to analyze the feasibility and award contracts to holons without constructing the whole model of a holarchy. [Copyright &y& Elsevier]

Abstract: In a recent paper (), an MPC algorithm for systems with stochastic multiplicative uncertainty was proposed. It offers potentially significant computational advantages and it is less conservative. In this note, a modification is suggested to strengthen the original result. [ABSTRACT FROM AUTHOR]