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The variability of renewable energies and their integration into the grid via power electronics demands the design of robust control algorithms. This work incorporates two techniques to ensure the stability of a boost converter through its state equations, implementing the inverse optimal control and the gain-scheduling technique for robust control settings. In such a way that, under a single adjustment, it is capable of damping different changes such as changes in the parameters, changes in the load, the input voltage, and the reference voltage. On the other hand, inverse optimal control is based on a discrete-time control Lyapunov function (CLF), and CLF candidate depends on fixed parameters that are selected to obtain the solution for inverse optimal control. Once these parameters have been found through heuristic or artificial intelligence methods, the new proposed methodology is capable of obtaining a robust optimal control scheme, without having to search for new parameters through other methods, since these are sometimes sensitive changes and many times the process of a new search is delayed. The results of the approach are simulated using Matlab, obtaining good performance of the proposed control under different operation conditions. Such simulations yielded errors of less than 1% based on the voltage reference, given the disturbances caused by changes in the input variables, system parameters, and changes in the reference. Thus, applying the new methodology, the stability of our system was preserved in all cases.

Cost functions have the potential to provide compact and understandable generalizations of motion. The goal of Inverse Optimal Control (IOC) is to analyze an observed behavior which is assumed to be optimal with respect to an unknown cost function, and infer this cost function. Here we develop a method for characterizing cost functions of legged locomotion, with the goal of representing complex humanoid behavior with simple models. To test this methodology we simulate walking gaits of a simple 5 link planar walking model which optimize known cost functions, and assess the ability of our IOC method to recover them. In particular, the IOC method uses an iterative trajectory optimization process to infer cost function weightings consistent with those used to generate a single demonstrated optimal trial. We also explore sensitivity of the IOC to sensor noise in the observed trajectory, imperfect knowledge of the model or task, as well as uncertainty in the components of the cost function used. With appropriate modeling, these methods may help infer cost functions from human data, yielding a compact and generalizable representation of human-like motion for use in humanoid robot controllers, as well as providing a new tool for experimentally exploring human preferences., Comment: 9 pages, 5 figures

Although rigorous framework exists for handling state variable inequality constraints under optimal control formulations, it is quite involved and difficult to incorporate for online use. In this study, an alternative approach is proposed by combining a state-dependent Riccati equation (SDRE) based inverse optimal control formulation with a set-theoretic barrier Lyapunov function (STBLF). Necessary derivations are presented. Both regulator and tracking type problems are considered. The performance of the proposed method is evaluated using numerical examples.

This paper proposes an inverse optimal control (IOC) framework which incorporates demonstrations with mixed qualities. The proposed method utilizes the benefits of sub-optimal demonstrations which can provide information about what not to do and supplies training data near states unvisited by optimal demonstrations. The main idea of the proposed method is to find the value function which satisfies the optimality condition over optimal demonstrations and violates it over sub-optimal demonstrations. We conduct experiments on three environments and empirically show that the proposed method outperforms the original IOC algorithm, which uses only optimal demonstrations.

The theory of optimal control has received considerable attention to model motion behavior or decision making of humans. Most approaches are based on a fixed (or infinite) time horizon which implies that all information is available at the beginning of the time interval. Nevertheless, it is reasonable to believe that the human uses information defined by a continuously moving information horizon at each time instant and adapts accordingly. Therefore, in this paper, we propose an optimal feedback control approach based on the paradigm of continuous updating. The model parameters which define individual human behavior consist of the cost function parameters and the length of the information horizon, which can be identified via a corresponding inverse optimal control approach. We show the applicability of the approach with simulations of a potential application example of human behavior identification from the point of view of a driving assistance system.

We consider bilevel optimization problems which can be interpreted as inverse optimal control problems. The lower-level problem is an optimal control problem with a parametrized objective function....

International audience; This study proposes an efficient and automatic tool to understand and analyze the human natural and fast gait tasks. First, the gait tasks are modeled as a nonlinear optimal control problem along with a nonlinear model predictive control, usually used in the humanoid robots control. Second, under the assumption that the walking motions are the result of an optimization process, the identification of plausible optimality criteria weight values is achieved with an inverse optimal control (IOC) approach. Our IOC walking scheme is performed on ten subjects with ten trials for each gait task considered. Results show that the variability observed in the experimental data are exhibited by our proposed scheme. Finally, an easy distinguish can be made between the gait tasks only by checking out the exhibited criteria weight values.

The object of this paper is to study the uniqueness of solutions of inverse control problems in the case where the dynamics is given by a control-affine system without drift and the costs are length and energy functionals.

International audience; A common assumption in physiology about human motion is that the realized movements are done in an optimal way. The problem of recovering of the optimality principle leads to the inverse optimal control problem. Formally, in the inverse optimal control problem we should find a cost function such that under the known dynamical constraint the observed trajectories are minimizing for such cost. In this paper we analyze the inverse problem in the case of finite horizon linear-quadratic problem. In particular, we treat the injectivity question, i.e. whether the cost corresponding to the given data is unique, and we propose a cost reconstruction algorithm. In our approach we define the canonical class on which the inverse problem is either unique or admit a special structure, which can be used in cost reconstruction.

In this paper, we consider the problem of computing parameters of a discrete-time infinite-horizon optimal control objective function from (possibly finite-length) state and control sequences. To solve this problem, we propose a novel method of inverse optimal control by exploiting a recently established infinite-horizon discrete-time minimum principle. Our proposed method admits a computationally efficient online implementation in which pairs of states and controls from the state and control sequences are processed sequentially without being stored or processed as a batch. We establish conditions guaranteeing the uniqueness of the cost-function parameters computed by our proposed method and illustrate its application in simulation.

In this paper, we consider the problem of computing parameters of an objective function for a discrete-time optimal control problem from state and control trajectories with active control constraints. We propose a novel method of inverse optimal control that has a computationally efficient online form in which pairs of states and controls from given state and control trajectories are processed sequentially without being stored or processed in batches. We establish conditions guaranteeing the uniqueness of the objective-function parameters computed by our proposed method from trajectories with active control constraints. We illustrate our proposed method in simulation.

In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observati ...

Epidemiological models constitute a fundamental means to understand the behavior and evolution of infectious diseases, as well as the mechanisms of action to counteract them. If an infectious disease spreads rapidly and affects a big population, it is vital to have effective control schemes that optimize the amount of available resources to mitigate the propagation of the disease, before it becomes a risk condition for public health systems. Inspired by this idea, we consider an extension of the SIR epidemic model and study the application of an impulsive control action to this system that minimizes vaccines and treatment given to population, using an inverse optimal control (IOC) approach.

In this note, we consider the problem of computing the parameters (or weights) of an optimal control objective function given optimal closed-loop state and control trajectories. We establish a method of inverse optimal control that exploits the discrete-time minimum principle. Under a testable matrix rank condition, our proposed method is guaranteed to recover the unknown objective-function parameters of finite-horizon discrete-time nonlinear optimal control problems.

Fahrer, die der Fahrsituation nicht genügend Aufmerksamkeit widmen, stellen eine Gefahr für die Verkehrssicherheit dar. Dies liegt daran, dass in diesem Fall das Fahrvermögen der Betroffenen deutlich verringert ist, was in Folge zu einem erhöhten Unfallrisiko führt. Deshalb versprechen Systeme, die die Fahreraufmerksamkeit automatisch beurteilen und entsprechend warnen oder eingreifen können, eine große Verbesserung der Verkehrssicherheit. Hierbei ist aber eine genaue und echtzeitfähige Beurteilung der Fahreraufmerksamkeit bezüglich des damit verbundenen Unfallrisikos erforderlich. Diese Dissertation führt eine neue Methode zur Beurteilung von Fahreraufmerksamkeit im situativen Kontext ein. Es wird vorgeschlagen angemessenes Blickverhalten durch Blickstrategien in einem entscheidungstheoretischen Formalismus festzulegen. In diesem Ansatz werden Modelle der Fahrsit- uation sowie der Wahrnehmung und der Fahrzeugführung des Fahrers verwendet. Bisherige Arbeiten beurteilen Fahreraufmerksamkeit zumeist alleine anhand Fahr- und Blickverhaltens. Ein deutlicher Nachteil ist dabei, dass somit das Zusammenspiel aus Fahrerverhalten, Fahrsituation und Unfallrisiko vernachlässigt wird. Das ist umso gravierender, da bekannt ist, dass erfahrene Fahrer an die Fahrsituation abgestimmte Blickstrategien zeigen, die die Beeinträchtigung ihrer Fahrleistung abmildern können. Ähnliche Blickstrategien enstehen auf natürliche Art und Weise aus dem gewählten entscheidungstheoretischen Ansatz. In der Arbeit wird der entscheidungstheoretische Ansatz beispielhaft an der Fahraufgabe des Spurhaltens untersucht. Hier wird auf die Modellbildung, die Echtzeitberechnung, die passende Parametrisierung sowie auf die Evaluierung der Methode in der Anwendung in einem neuen Warnsystem eingegangen. Zuerst wird die Aufgabe des Spurhaltens bei einer Nebenaufgabe, die um die visuelle Aufmerksamkeit konkurriert, modelliert. Dazu wird ein Partially Observable Markov Decision Process (POMDP) verwendet, der ein kinematisches Model der Fahraufgabe, ein Model der sensorischen Eigenschaften des Fahrers sowie ein Modell der Nebenaufgabe enthält. Danach wird die Berechnung von Strategien in dem POMDP untersucht. Diese Strategien dienen dazu das angemessene Blickverhalten festzulegen. Schließlich wird die Wirklichkeitstreue dieser Strategien überprüft und der erforderliche Rechenaufwand analysiert. Zweitens wird die Wahl einer passenden Belohnungsfunktion betrachtet. Diese ist deswegen von Bedeutung, da sie schlussendlich das angemessene Blickverhalten festlegt. Es wird ein neues Verfahren der inversen optimalen Steuerung entwickelt, das es vermag Parameter der Belohnungsfunktion aus dem Verhalten erfahrener Fahrer zu schätzen. In einem Experiment im Realverkehr erhobenes Fahrerverhalten wird benutzt um die entwickelte Methode hinsichtlich der Genauigkeit in der Verhaltensvorhersage zu prüfen. Die vorliegende Arbeit untersucht drittens die Schätzung von Modellen der sensorischen Eigenschaften von Fahrern. Dazu wird der erste allgemeine Ansatz für dieses Inferenzproblem in sequenziellen Entscheidungsproblemen vorgestellt. Darauffolgend wird eine Umsetzung des Ansatzes für den vorherig eingeführten POMDP entwickelt. Das resultierende Verfahren wird mittels Fahrverhaltensdaten aus einem weiteren Fahrversuch geprüft. Schließlich wird viertens die Entwicklung eines Warnsystems und dessen Einbindung in ein Versuchsfahrzeug verfolgt. Das System zielt darauf ab den Fahrer bei der Aufrechterhaltung von genügen Aufmerksamkeit zu unterstützen. In einem abschließenden Nutzertest wird das entwickelte System mit einem Warnsystem nach dem aktuellen Stand der Technik verglichen, wobei sowohl die Akzeptanz durch die Nutzer als auch die Auswirkungen auf die Fahrleistung untersucht werden. Im Ganzen verdeutlicht diese Arbeit die Umsetzbarkeit und die Vorteile des verfolgten Ansatzes des angemessenen Blickverhaltens für die automatische Bewertung von Fahreraufmerksamkeit. Es wurde gezeigt, dass der benötigte Rechenaufwand eine Echtzeitanwendung zulässt und dass geeignete Modellparameter automatisch geschätzt werden können. Schließlich wurde die Verbesserung eines Ablenkungswarnsystems belegt. Folglich stellt die Methodologie, die in dieser Arbeit eingeführt wurde, einen vielversprechenden neuen Ansatz zur Bewertung von Fahreraufmerksamkeit dar, der die Probleme des aktuellen Standes der Technik vermeidet.

We formulate and solve an inverse optimal control problem that allows us to study human gait based on motion capture data and a template model that is defined by a simple mechanical model of walking with two elastic legs. To this end we derive an optimal control model that consists of two parts: a three-dimensional template walker and an objective, defined by a linear combination of physically meaningful optimization criteria known from humanoid robotics. Based on a direct all-at-once approach we identify the objective weights such that the resulting optimal gait fits real human motion data as closely as possible. Considering knee actuation, foot placement and phase duration as controls we identify the optimal weights for six different trials on level ground from two very different subjects. In future work the identified criteria will be used to simulate optimized human gait and to generate reference trajectories for humanoid gait control.

This paper presents an inverse optimal control approach in order to achieve stabilization of discrete-time nonlinear systems, avoiding the need to solve the associated Hamilton–Jacobi–Bellman equation, and minimizing a cost functional. Then, the proposed approach is extended to discrete-time disturbed nonlinear systems. The synthesized stabilizing optimal controller is based on a discrete-time control Lyapunov function. The applicability of the proposed approach is illustrated via simulations.

La optimización aplicada al control automático permite obtener acciones de control que satisfacen no solo el objetivo de control, sino también la minimización de un determinado funcional de costo. Dinámicas complejas dificultan hallar la solución explícita de un problema de control óptimo. El control óptimo inverso evita la solución explícita de la ecuación de Hamilton-Jacobi-Bellman para determinar la ley óptima de control. Ilustrar la potencialidad del control óptimo inverso como alternativa para resolver problemas complejos de optimización en control. Se describe el problema de control óptimo para motivar el control óptimo inverso. Se formulan resultados matemáticos generales y se ilustra su aplicación a través de casos de ejemplo. Las formulaciones matemáticas presentadas son probadas analíticamente en casos del tipo óptimo cuadrático lineal (LQR) y óptimo inverso basado en funciones de control de Lyapuvov (LCF). Es posible formular un problema de control óptimo para sistemas de tipo no lineal, sin abordar la solución explícita del problema de optimización, mediante control óptimo inverso.

Differentiating the ability from the motivation to act is of central importance to psychiatric disorders in general and depression in particular. However, it has been difficult to develop quantitative approaches to relate depression to poor motor performance in goal-directed tasks. Here, we use an inverse optimal control approach to provide a computational framework that can be used to infer and factorize performance deficits into three components: sensorimotor speed, goal setting and motivation. Using a novel computer-simulated driving experiment, we found that (1) severity of depression is associated with both altered sensorimotor speed and motivational function; (2) moderately to severely depressed individuals show an increased distance from the stop sign indicating aversive learning affecting goal setting functions. Taken together, the inverse optimal control framework can disambiguate on an individual basis the sensorimotor from the motivational dysfunctions in depression, which may help to develop more precisely targeted interventions.

In this paper, we consider the problem of estimating the parameters of an optimal control objective function based on measurements of the closed loop system. In contrast to previous work on inverse optimal control, we consider measurements that are noise-corrupted and contain only partial-state information. We propose an inverse optimal control method based on a new soft-optimality constrained methodology of state estimation. We establish a sufficient condition for recovery of the unknown objective function parameters given complete-state information, and develop results characterising the performance of our method for linear systems. We illustrate our proposed soft-optimality approach through simulations of a nonlinear and fully-actuated mechanical system.

Inverse optimal trajectory tracking via a control Lyapunov function (CLF) for discrete time non-linear systems is developed and applied to type 1 diabetes mellitus patients control. The control law calculates the insulin delivery rate in order to prevent hyperglycemia and hypoglycemia levels. To synthesize the inverse optimal control law a quadratic candidate CLF is used. The proposed algorithm is tuned to follow a desired trajectory; this trajectory reproduces the glucose absorption of a healthy person. Simulation results applied for two different patients illustrate the applicability of the control law and a comparison with inverse optimal neural control via passivity is included.

A class of optimal control problems having an optimal solution of a specified property is investigated. Examples from irreversible thermodynamics and microeconomics are given. Such a formulation, as has been shown, can be regarded as an inverse optimal control problem.

The study of emotional facial expressions and of emotional body language is currently receiving a lot of attention in various research areas. In this research, we study implicit bodily expression of emotions during standard motions such as walking forwards. An underlying assumption of our work is that all human motion is optimal in some sense and that different emotions induce different objective functions, which result in different deformations of normal motion. We created a 2-D rigid-body model of a human for which we use its dynamics simulation in an optimal control context. This approach allows us to obtain different styles of motion by using different objective criteria. We present the model, the optimal control problem formulation and the direct multiple-shooting method that efficiently solves this problem. The results of this work form the foundation for further analysis of emotional motions using inverse optimal control methods.

In this chapter we study an inverse optimal control problem in discrete-time stochastic control. We give necessary and sufficient conditions for a solution to a system of stochastic difference equations to be the solution of a certain OCP. Our results extend to the stochastic case the work of Dechert [21]. In particular, we present a stochastic version of an important principle in welfare economics. The presentation of this chapter is based on Gonzalez–Sanchez and Hernandez–Lerma [36].

This paper is devoted to the general problem of reconstructing the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular classes of control systems and of costs under consideration. To summarize, our conclusion is that in general, inside these classes, three experiments visiting the same values of the control are needed to reconstruct the cost, and two experiments are in general not enough. The method is constructive. The proof of these results is mostly based upon the Thom's transversality theory.

International audience; This paper discusses forward and inverse optimal control problems for bipedal human-like running, with a focus on inverse optimal control. The (forward) optimal control problem looks for the optimal solution for a problem formulation, i.e. given objective function and given dynamic constraints. The inverse optimal control problem is more challenging and consists in determining the objective function and potentially unknown parts in the dynamic model that best reproduce a solution that is known from measurements. Periodic running motions are modeled as hybrid dynamic models with multiple phases and discontinuities, based on a three-dimensional multibody system model with 25 degrees of freedom.We investigate a recorded running motion on a treadmill at 10 km/h running speed and identify the best possible objective function based on some hypotheses for potential contributions to this objective function. For this, we apply a previously developed inverse optimal control technique which uses a combination of a direct multiple shooting method and a derivative-free optimization techniqueand we demonstrate here that it also works for problems of the given complexity.

This paper deals with finite time inverse optimal control for affine nonlinear systems. Based on control Lyapunov functions, a universal control formula is presented to ensure that the closed-loop system is finite time stable. From this, less conservative conditions for the finite time inverse optimal control are derived. A finite time inverse optimal control law that minimizes the cost functional is designed. A numerical example is used to illustrate the effectiveness of the proposed design technique.