On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)

The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly's dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. The efficacy of the proposed bound is demonstrated on an inventory management example.Comment: Accepted for publication at Automatic

Robust Model Predictive Control via Scenario Optimization

This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to non-convex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this paper is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a-priori assigned probability p, while the system's state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.Comment: This manuscript is a preprint of a paper accepted for publication in the IEEE Transactions on Automatic Control, with DOI: 10.1109/TAC.2012.2203054, and is subject to IEEE copyright. The copy of record will be available at http://ieeexplore.ieee.or

The Effect of Active and Passive Control on Air Traffic Controller Dynamic Memory

The purpose of this study was to investigate the effect of automated and passive control on air traffic controller dynamic memory. The study consisted of two experiments, each involving a realistic ATC scenario for radar approach control with a mix of arriving and departing traffic. In Experiment I, the subjects performed manual control of the traffic while, in Experiment II, the scenario was highly automated and the subjects were tasked with only monitoring the situation. The dynamic memory performance was measured by interrupting the scenario and having the subjects recall the traffic situation at the moment of simulation interruption. The accuracy of recall was compared between the manual and automated scenarios. It was anticipated that subjects exercising manual control would have superior recall ability and a picture. This would have significant implications on the design of automated systems for ATC and the role of the human controller within the ATC system

An accessibility planning tool for network transit oriented development: SNAP

In the academic debate regarding the influences between urban form, built environment and travel patterns, a specific idea that has taken hold is that more compact urban development around railway stations, often referred to as Transit Oriented Development (TOD), contributes to the control of vehicle travel and to more sustainable metropolitan systems. According to this general principle this work proposes a GIS accessibility tool for the design of polycentric transit oriented scenario: SNAP - Station Network Accessibility Planning tool. In the first part the state of the art on Transit Oriented Development policies in Europe is presented with a focus on three study cases. In the second part the SNAP tool is described, with remarks to the approach, the methodology and the used indicators. Furthermore the paper discusses an application to the metropolitan area of Naples

Experience Transfer for Robust Direct Data-Driven Control

Learning-based control uses data to design efficient controllers for specific systems. When multiple systems are involved, experience transfer usually focuses on data availability and controller performance yet neglects robustness to variations between systems. In contrast, this letter explores experience transfer from a robustness perspective. We leverage the transfer to design controllers that are robust not only to the uncertainty regarding an individual agent's model but also to the choice of agent in a fleet. Experience transfer enables the design of safe and robust controllers that work out of the box for all systems in a heterogeneous fleet. Our approach combines scenario optimization and recent formulations for direct data-driven control without the need to estimate a model of the system or determine uncertainty bounds for its parameters. We demonstrate the benefits of our data-driven robustification method through a numerical case study and obtain learned controllers that generalize well from a small number of open-loop trajectories in a quadcopter simulation

Stabilisation of state-and-input constrained nonlinear systems via diffeomorphisms: A Sontag's formula approach with an actual application

In this work, we provide a new and constructive outlook for the control of state-and-input constrained nonlinear systems. Previously, explicit solutions have been mainly focused on the finding of a barrier-like Lyapunov function, whereas we propose the construction of a diffeomorphism to map all the trajectories of the constrained dynamics into an unconstrained one. Careful analysis has revealed that only some foundations of differential geometry and a technical assumption are necessary to construct the proposed methodology based on the well-established theories of control Lyapunov functions and Sontag's universal formulae. Altogether, it allows us to obtain an explicit solution that even includes bounded constraints in the control action, giving the designer a way to decide (to some extent) the trade-off between control saturations and robustness. Moreover, this approach does not rely on the own structure of the system dynamics, therefore covering a broad class of nonlinear systems. The main advantage of this approach is that the use of a diffeomorphism allows the splitting of the mathematical treatment of the constraint and the Lyapunov controller design. The result has been successfully applied to solve the dynamic positioning of an actual ship, where the nonlinear state constraints describe a strait. This approach enabled us to design a control Lyapunov function and thereby use Sontag's formula to solve the stabilisation problem. Realistic simulations have been executed in a real scenario on the simulator owned by an international shipbuilding company.Postprint (author's final draft