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This article proposes a hierarchical learning architecture for safe data-driven control in unknown environments. We consider a constrained nonlinear dynamical system and assume the availability of state-input trajectories solving control tasks in different environments. In addition to task-invariant system state and input constraints, a parameterized environment model generates task-specific state constraints, which are satisfied by the stored trajectories. Our goal is to use these trajectories to find a safe and high-performing policy for a new task in a new, unknown environment. We propose using the stored data to learn generalizable control strategies. At each time step, based on a local forecast of the new task environment, the learned strategy consists of a target region in the state space and input constraints to guide the system evolution to the target region. These target regions are used as terminal sets by a low-level model predictive controller. We show how to i) design the target sets from past data and then ii) incorporate them into a model predictive control scheme with shifting horizon that ensures safety of the closed-loop system when performing the new task. We prove the feasibility of the resulting control policy, and apply the proposed method to robotic path planning, racing, and computer game applications. Note to Practitioners—This paper was motivated by the challenge of designing safe controllers for autonomous systems navigating through new environments. We consider scenarios where trajectory data from control tasks in different environments is available to the control designer. Possible applications include autonomous vehicles racing on new tracks or robotic manipulators performing tasks in the presence of new obstacles. Existing approaches to model-based control design for new environments generally use trajectory libraries, systematically adapting stored trajectories to the constraints of the new environment. This typically requires a priori knowledge of the entire task environment as well as resources to store and maintain the growing library. This paper suggests a new hierarchical control approach, in which stored trajectories are used to learn high-level strategies that can be applied while solving the new task. The strategies are learned offline, and only the parameterized strategy function needs to be stored for online control. Strategies only require knowledge of the nearby task environment, and provide navigation guidelines for the system. In this paper we show how to find such strategies from previous task data and how to integrate them into a low-level controller to safely and efficiently solve the new task. We also show how to adapt the modular framework as needed for a user’s desired application. Simulation experiments in robotic manipulator, autonomous vehicle, and computer game examples suggest that our approach can be used in a wide range of applications. In future research, we will address how to adapt the method for time-varying or stochastic environments. [ABSTRACT FROM AUTHOR]

We present a framework for autonomous driving which can learn from human demonstrations, and we apply it to the longitudinal control of an autonomous car. Offline, we model car-following strategies from a set of example driving sequences. Online, the model is used to compute accelerations which replicate what a human driver would do in the same situation. This reference acceleration is tracked by a predictive controller which enforces a set of comfort and safety constraints before applying the final acceleration. The controller is designed to be robust to the uncertainty in the predicted motion of the preceding vehicle. In addition, we estimate the confidence of the driver model predictions and use it in the cost function of the predictive controller. As a result, we can handle cases where the training data used to learn the driver model does not provide sufficient information about how a human driver would handle the current driving situation. The approach is validated using a combination of simulations and experiments on our autonomous vehicle. [ABSTRACT FROM AUTHOR]

Driving requires forecasts. Forecasted movements of objects in the driving scene are uncertain. Inevitably, decision and control algorithms for autonomous driving need to cope with such uncertain forecasts. In assisted driving, the uncertainty in the human/vehicle interaction further increases the complexity of the control design task. Our research over the past ten years has focused on control design methods which systematically handle uncertain forecasts for autonomous and semi-autonomous vehicles. This paper presents an overview of our findings and discusses relevant aspects of our recent results. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the control of distributed storage networks with guarantees of constraints satisfaction and asymptotic stability. We consider two problems: network capacity maximization and network balancing. In the first part of the paper we describe the two problems, highlight their importance in a wide number of engineering applications, and compare them by analyzing the properties of their solutions. In the second part we present algorithms for solving both problems by using a convex one-step model predictive controller (MPC) which guarantees persistent state and flow constraints satisfaction. We present simple conditions which link the network topology, the MPC weights and the asymptotic stability of the closed-loop system. A numerical example illustrates the effectiveness of the proposed approach. [Copyright &y& Elsevier]

We study the problem of heating, ventilation and air conditioning (HVAC) control in a typical commercial building. We propose a model predictive control (MPC) approach which minimizes energy cost while satisfying occupant comfort and control actuator constraints, using a simplified system model and incorporating predictions of future weather and occupancy inputs. In simplified physics-based models of HVAC systems, the product between air temperatures and flow rates arising from energy balance equations leads to a non-convex MPC problem. Fast computational techniques for solving non-convex optimization can only provide certificates of local optimality. Local optima can potentially cause MPC to have worse performance than existing control implementations, so deserve careful consideration. The objective of this article is to investigate the phenomenon of local optima in the MPC optimization problem for a simple HVAC system model. In the first part of the article, simplified physics-based models and MPC design for two common HVAC configurations are introduced. In the second part, simulation results exhibiting local optima for both configurations are presented. We perform a detailed analysis on the different types of local optima and their physical interpretation. We then use this analysis to derive physics-based rules to exclude classes of locally optimal control sequences under specific conditions. [ABSTRACT FROM AUTHOR]

Abstract: Finite-time optimal control problems with quadratic performance index for linear systems with linear constraints can be transformed into Quadratic Programs (QPs). Model Predictive Control requires the on-line solution of such QPs. This can be obtained by using a QP solver or evaluating the associated explicit solution. The objective of this note is twofold. First, we shed some light on the computational complexity and storage demand of the two approaches when an active set QP solver is used. Second, we show the existence of alternative algorithms with a different tradeoff between memory and computational time. In particular, we present an algorithm which, for a certain class of systems, outperforms standard explicit solvers both in terms of memory and worst case computational time. [Copyright &y& Elsevier]

Abstract: This work addresses the problem of offset-free Model Predictive Control (MPC) when tracking an asymptotically constant reference. In the first part, compact and intuitive conditions for offset-free MPC control are introduced by using the arguments of the internal model principle. In the second part, we study the case where the number of measured variables is larger than the number of tracked variables. The plant model is augmented only by as many states as there are tracked variables, and an algorithm which guarantees offset-free tracking is presented. In the last part, offset-free tracking properties for special implementations of MPC schemes are briefly discussed. [Copyright &y& Elsevier]

Abstract: We present a methodology for designing reference tracking controllers for constrained, discrete-time piecewise affine systems. The approach follows the idea of reference governor techniques where the desired set-point is filtered by a system called the “reference governor”. Based on the system current state, set-point, and prescribed constraints, the reference governor computes a new set-point for a low-level controller so that the state and input constraints are satisfied and convergence to the original set-point is guaranteed. In this note we show how to design a reference governor for constrained piecewise affine systems by using polyhedral invariant sets, reachable sets, multiparametric programming and dynamic programming techniques. [Copyright &y& Elsevier]

In this paper, we propose a path following Model Predictive Control-based (MPC) scheme utilising steering and braking. The control objective is to track a desired path for obstacle avoidance manoeuvre, by a combined use of braking and steering. The proposed control scheme relies on the Nonlinear MPC (NMPC) formulation we used in [F. Borrelli, et al., MPC-based approach to active steering for autonomous vehicle systems, Int. J. Veh. Autonomous Syst. 3(2/3/4) (2005), pp. 265-291.] and [P. Falcone, et al., Predictive active steering control for autonomous vehicle systems, IEEE Trans. Control Syst. Technol. 15(3) (2007), pp. 566-580.]. In this work, the NMPC formulation will be used in order to derive two different approaches. The first relies on a full tenth-order vehicle model and has high computational burden. The second approach is based on a simplified bicycle model and has a lower computational complexity compared to the first. The effectiveness of the proposed approaches is demonstrated through simulations and experiments. [ABSTRACT FROM AUTHOR]

In this paper, a model predictive control (MPC) approach for controlling an active front steering system in an autonomous vehicle is presented. At each time step, a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to follow the trajectory on slippery roads at the highest possible entry speed. We present two approaches with different computational complexities. In the first approach, we formulate the MPC problem by using a nonlinear vehicle model. The second approach is based on successive online linearization of the vehicle model. Discussions on computational complexity and performance of the two schemes are presented. The effectiveness of the proposed MPC formulation is demonstrated by simulation and experimental tests up to 21 m/s on icy roads. [ABSTRACT FROM AUTHOR]

This paper describes a hybrid model and a model predictive control (MPC) strategy for solving a traction con- trol problem. The problem is tackled in a systematic way from modeling to control synthesis and implementation. The model is described first in the Hybrid Systems Description Language to obtain a mixed-logical dynamical (MLD) hybrid model of the open-loop system. For the resulting MLD model, we design a receding horizon finite-time optimal controller. The resulting optimal controller is converted to its equivalent piecewise affine form by employing multiparametric programming techniques, and finally experimentally tested on a car prototype. Experiments show that good and robust performance is achieved in a limited development time by avoiding the design of ad hoc supervisory and logical constructs usually required by controllers developed according to standard techniques. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for computing the solution to the constrained infinite-time, linear quadratic regulator (CLQR) problem for discrete time systems. The algorithm combines multi-parametric quadratic programming with reachability analysis to obtain the optimal piecewise affine (PWA) feedback law. The algorithm reduces the time necessary to compute the PWA solution for the CLQR when compared to other approaches. It also determines the minimal finite horizon N¯S, such that the constrained finite horizon LQR problem equals the CLQR problem for a compact set of states S. The on-line computational effort for the implementation of the CLQR can be significantly reduced as well, either by evaluating the PWA solution or by solving the finite dimensional quadratic program associated with the CLQR for a horizon of N=N¯S. [Copyright &y& Elsevier]

Buildings that use radiant slab systems with evaporative cooling sources have shown to be energy efficient. However, control of the systems is challenging because of the slow response of the slab and the limited capacity of cooling sources. The objectives of this paper are to: (1) create a simplified dynamic model of radiant slab system for implementation in real-time model predictive controller (MPC); and (2) test the MPC energy and thermal comfort performance in a case study building. A calibrated EnergyPlus model of the building was developed as the testbed. The MPC is compared with the existing rule-based control method for a cooling season in a dry and hot climate. The results indicated that the MPC controller was able to maintain zone operative temperatures at EN 15251 Category II level more than 95% of the occupied hours for all zones, while with the rule-based method, only the core zone were maintained at this thermal comfort level. Compared to the rule-based method, MPC reduced the cooling tower energy consumption by 55% and pumping power consumption by 25%. [ABSTRACT FROM AUTHOR]