arXiv subjects

Mircea Lazar

Publications and source records attributed to Mircea Lazar.

At least 55 records · Page 3Linked to original sources

arXiv2023

Physics-guided neural networks for inversion-based feedforward control applied to hybrid stepper motors

Rotary motors, such as hybrid stepper motors (HSMs), are widely used in industries varying from printing applications to robotics. The increasing need for productivity and efficiency without increasing the manufacturing costs calls for innovative control design. Feedforward control is typically used in tracking control problems, where the desired reference is known in advance. In most applications, this is the case for HSMs, which need to track a periodic angular velocity and angular position reference. Performance achieved by feedforward control is limited by the accuracy of the available model describing the inverse system dynamics. In this work, we develop a physics-guided neural network (PGNN) feedforward controller for HSMs, which can learn the effect of parasitic forces from data and compensate for it, resulting in improved accuracy. Indeed, experimental results on an HSM used in printing industry show that the PGNN outperforms conventional benchmarks in terms of the mean-absolute tracking error.

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arXiv2023

Data-driven feedforward control design for nonlinear systems: A control-oriented system identification approach

Feedforward controllers typically rely on accurately identified inverse models of the system dynamics to achieve high reference tracking performance. However, the impact of the (inverse) model identification error on the resulting tracking error is only analyzed a posteriori in experiments. Therefore, in this work, we develop an approach to feedforward control design that aims at minimizing the tracking error a priori. To achieve this, we present a model of the system in a lifted space of trajectories, based on which we derive an upperbound on the reference tracking performance. Minimization of this bound yields a feedforward control-oriented system identification cost function, and a finite-horizon optimization to compute the feedforward control signal. The nonlinear feedforward control design method is validated using physics-guided neural networks on a nonlinear, nonminimum phase mechatronic example, where it outperforms linear ILC.

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arXiv2023

On a Canonical Distributed Controller in the Behavioral Framework

Control in a classical transfer function or state-space setting typically views a controller as a signal processor: sensor outputs are mapped to actuator inputs. In behavioral system theory, control is simply viewed as interconnection; the interconnection of a plant with a controller. In this paper we consider the problem of control of interconnected systems in a behavioral setting. The behavioral setting is especially fit for modelling interconnected systems, because it allows for the interconnection of subsystems without imposing inputs and outputs. We introduce a so-called canonical distributed controller that implements a given interconnected behavior that is desired, provided that necessary and sufficient conditions hold true. The controller design can be performed in a decentralized manner, in the sense that a local controller only depends on the local system behavior. Regularity of interconnections is an important property in behavioral control that yields feedback interconnections. We provide conditions under which the interconnection of this distributed controller with the plant is regular. Furthermore, we show that the interconnections of subsystems of the canonical distributed controller are regular if and only if the interconnections of the plant and desired behavior are regular.

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arXiv2022

Consensus of hierarchical multi-agent systems with a time-varying set of active agents

Time-varying hierarchical multi-agent systems are common in many applications. A well-known solution to control these systems is to use state feedback controllers that depend on the adjacency matrix to reach consensus. This solution has been applied so far to multi-agent systems with fixed or time-varying communication topologies. In this paper, we consider single-integrator multi-agent systems where only a subset of the agents are active at any given time and the set of active agents is time-varying. This type of multi-agent system is relevant in applications such as modular multilevel converters and water pumping systems. We develop a switching algorithm that periodically selects a set of active agents through a set of graphs that connect the follower agents with a leader agent. We further prove that the developed switching algorithm combined with a classic consensus protocol yields convergence to a consensus state defined by the leader despite a time-varying set of active agents. The effectiveness of the switching algorithm is illustrated in two benchmark examples: a modular multilevel converter and a water pumping system.

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arXiv2022

On the Steady-State Behavior of Finite-Control-Set MPC with an Application to High-Precision Power Amplifiers

Motivated by increasing precision requirements for switched power amplifiers, this paper addresses the problem of model predictive control (MPC) design for discrete-time linear systems with a finite control set (FCS). Typically, existing solutions for FCS-MPC penalize the output tracking error and the control input rate of change, which can lead to arbitrary switching among the available discrete control inputs and unpredictable steady-state behavior. To improve the steady-state behavior of FCS-MPC, in this paper we design a cost function that penalizes the tracking error with respect to a state and input steady-state limit cycle. We prove that if a suitable terminal cost is added to the FCS-MPC algorithm convergence to the limit cycle is ensured. The developed methodology is validated in direct switching control of a power amplifier for high-precision motion systems, where it significantly improves the steady-state output current ripple.

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arXiv2022

Physics-guided neural networks for feedforward control: From consistent identification to feedforward controller design

Model-based feedforward control improves tracking performance of motion systems, provided that the model describing the inverse dynamics is of sufficient accuracy. Model sets, such as neural networks (NNs) and physics-guided neural networks (PGNNs) are typically used as flexible parametrizations that enable accurate identification of the inverse system dynamics. Currently, these (PG)NNs are used to identify the inverse dynamics directly. However, direct identification of the inverse dynamics is sensitive to noise that is present in the training data, and thereby results in biased parameter estimates which limit the achievable tracking performance. In order to push performance further, it is therefore crucial to account for noise when performing the identification. To address this problem, this paper proposes the use of a forward system identification using (PG)NNs from noisy data. Afterwards, two methods are proposed for inverting PGNNs to design a feedforward controller for high-precision motion control. The developed methodology is validated on a real-life industrial linear motor, where it showed significant improvements in tracking performance with respect to the direct inverse identification.

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arXiv2022

Long hauling eco-driving: heavy-duty trucks operational modes control with integrated road slope preview

In this paper, a complete eco-driving strategy for heavy-duty trucks (HDT) based on a finite number of driving modes with corresponding gear shifting is developed to cope with different route events and with road slope data. The problem is formulated as an optimal control problem with respect to fuel consumption and trip duration, and solved using a Pontryagin minimum principle (PMP) algorithm for a path search problem, such that computations can be carried out online, in real-time. The developed eco-driving assistance system (EDAS) provides a velocity profile and a sequence of driving modes (and gears) recommendation to the driver, without actively controlling the HDT (human in the loop) and, in practice, allows contextual feedback incorporation from the driver for safety. Simulation results show that the developed methodology is able to provide a velocity profile for a complete route based on known road events and slope information while satisfying all truck operational constraints.

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arXiv2022

On data-driven control: informativity of noisy input-output data with cross-covariance bounds

In this paper we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, $\mathcal{H}_\infty$ and $\mathcal{H}_2$ control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.

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arXiv2022

Stabilization of discrete-time nonlinear systems based on control dissipation functions

This paper develops a dissipativity-based framework for synthesis of stabilizing controllers for discrete-time nonlinear systems subject to state/input constraints. Firstly, we revisit dissipation inequalities for discrete-time nonlinear systems that involve general storage and supply functions. We prove that positive definite storage functions and cyclically negative supply functions yield asymptotic Lyapunov stability. Secondly, we define control dissipation functions (CDFs) and we construct stabilizing receding horizon controllers by minimizing CDFs subject to a cyclically negative supply condition. The effectiveness of stabilizing controllers based on CDFs is demonstrated on stabilization of interconnected synchronous generators with nonlinear coupling and state/input constraints.

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arXiv2022

Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds

Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and $\mathcal{H}_2$/$\mathcal{H}_\infty$ control through vertex/half-space representations of the polyhedral set of unfalsified systems.

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arXiv2022

An Efficient MPC Algorithm For Switched Systems with Minimum Dwell Time Constraints

This paper presents an efficient suboptimal model predictive control (MPC) algorithm for nonlinear switched systems subject to minimum dwell time constraints (MTC). While MTC are required for most physical systems due to stability, power and mechanical restrictions, MPC optimization problems with MTC are challenging to solve. To efficiently solve such problems, the on-line MPC optimization problem is decomposed into a sequence of simpler problems, which include two nonlinear programs (NLP) and a rounding step, as typically done in mixed-integer optimal control (MIOC). Unlike the classical approach that embeds MTC in a mixed-integer linear program (MILP) with combinatorial constraints in the rounding step, our proposal is to embed the MTC in one of the NLPs using move blocking. Such a formulation can speedup on-line computations by employing recent move blocking algorithms for NLP problems and by using a simple sum-up-rounding (SUR) method for the rounding step. An explicit upper bound of the integer approximation error for the rounding step is given. In addition, a combined shrinking and receding horizon strategy is developed to satisfy closed-loop MTC. Recursive feasibility is proven using a $l$-step control invariant ($l$-CI) set, where $l$ is the minimum dwell time step length. An algorithm to compute $l$-CI sets for switched linear systems off-line is also presented. Numerical studies show significant speed-up and comparable control performance of the proposed MPC algorithm against the classical approach, though at the cost of sub-optimal solutions.

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arXiv2022

On feedforward control using physics-guided neural networks: Training cost regularization and optimized initialization

Performance of model-based feedforward controllers is typically limited by the accuracy of the inverse system dynamics model. Physics-guided neural networks (PGNN), where a known physical model cooperates in parallel with a neural network, were recently proposed as a method to achieve high accuracy of the identified inverse dynamics. However, the flexible nature of neural networks can create overparameterization when employed in parallel with a physical model, which results in a parameter drift during training. This drift may result in parameters of the physical model not corresponding to their physical values, which increases vulnerability of the PGNN to operating conditions not present in the training data. To address this problem, this paper proposes a regularization method via identified physical parameters, in combination with an optimized training initialization that improves training convergence. The regularized PGNN framework is validated on a real-life industrial linear motor, where it delivers better tracking accuracy and extrapolation.

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arXiv2021

Guaranteed $\mathcal{H}_\infty$ performance analysis and controller synthesis for interconnected linear systems from noisy input-state data

The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that lends itself well to distributed controller synthesis from data. Sufficient LMI conditions based on noisy data are provided for the existence of a dynamic distributed controller that achieves $\mathcal{H}_\infty$ performance. The presented approach enables scalable analysis and control of large-scale interconnected systems from noisy input-state data sets.

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arXiv2021

Physics-Guided Neural Networks for Inversion-based Feedforward Control applied to Linear Motors

Ever-increasing throughput specifications in semiconductor manufacturing require operating high-precision mechatronics, such as linear motors, at higher accelerations. In turn this creates higher nonlinear parasitic forces that cannot be handled by industrial feedforward controllers. Motivated by this problem, in this paper we develop a general framework for inversion-based feedforward controller design using physics-guided neural networks (PGNNs). In contrast with black-box neural networks, the developed PGNNs embed prior physical knowledge in the input and hidden layers, which results in improved training convergence and learning of underlying physical laws. The PGNN inversion-based feedforward control framework is validated in simulation on an industrial linear motor, for which it achieves a mean average tracking error twenty times smaller than mass-acceleration feedforward in simulation.

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arXiv2021

Scalable distributed and decentralized $\mathscr{H}_2$ controller synthesis for interconnected linear discrete-time systems

The current limitation in the synthesis of distributed $\mathscr{H}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed $\mathscr{H}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complexity compared to the corresponding centralized $\mathscr{H}_2$ controller synthesis problem. Additionally, the developed conditions are adapted for the corresponding decentralized $\mathscr{H}_2$ controller synthesis problem with fixed supply functions for the interconnections. The effectiveness and scalability of the developed distributed $\mathscr{H}_2$ controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph.

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arXiv2020

Data-driven distributed control: Virtual reference feedback tuning in dynamic networks

In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the controller class contains the ideal distributed controller. The developed distributed controller synthesis method is illustrated on an academic example network of nine subsystems and the influence of the controller interconnection structure on the achieved closed-loop performance is analyzed.

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arXiv2019

Heterogeneously parameterized tube model predictive control for LPV systems

This paper presents a heterogeneously parameterized tube-based model predictive control (MPC) design applicable to linear parameter-varying (LPV) systems. In a heterogeneous tube, the parameterizations of the tube cross sections and the associated control laws are allowed to vary along the prediction horizon. Two extreme cases that can be described in this framework are scenario MPC (high complexity, larger domain of attraction) and homothetic tube MPC with a simple time-invariant control parameterization (low complexity, smaller domain of attraction). In the proposed framework, these extreme parameterizations, as well as other parameterizations of intermediate complexity, can be combined within a single tube. By allowing for more flexibility in the parameterization design, one can influence the trade-off between computational cost and the size of the domain of attraction. Sufficient conditions on the parameterization structure are developed under which recursive feasibility and closed-loop stability are guaranteed. A specific parameterization that combines the principles of scenario and homothetic tube MPC is proposed and it is shown to satisfy the required conditions. The properties of the approach, including its capability of achieving improved complexity/performance trade-offs, are demonstrated using two numerical examples.

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arXiv2018

A recursive estimation approach to distributed identification of large-scale multi-input-single-output FIR systems

The problem of identifying single modules in multiple-input-single-output (MISO) systems is considered. A novel approach to distributed identification of MISO finite impulse response systems is presented. The distributed identification is discerned by the local estimation of local parameters, which correspond to a module in the MISO system. The local estimators are derived from the standard recursive least squares estimator and require limited information exchange. By Lyapunov's second method, sufficient conditions are derived for asymptotic convergence of the estimators to the true parameters in the absence of disturbances, which lead to asymptotic unbiasedness in the presence of additive output disturbances.

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