Nominal System Research Articles

Robust error feedback output regulation of a 2 × 2 hyperbolic system

Abstract In this paper, we consider the robust error feedback output regulation problem for a linear $ 2 \times 2 $ hyperbolic system with system uncertainties and disturbance signals. Using the backstepping method, the state feedback controller for the system without the system uncertainties and the external disturbance signals (nominal system) is designed. In terms of the measurable regulation error, an observer system is designed to recover the state of the nominal system, and an observer-based error feedback controller is obtained to solve the robust output regulation problem. Moreover, we prove that the controller is robust to the system uncertainties and the disturbance signals, and show that the state of the closed-loop system is bounded. The numerical simulations are presented to illustrate the effectiveness of the theoretical results.

A comparative study of nominal group systems and structures between Lhasa Tibetan and Mandarin Chinese

Abstract This paper presents a text-based comparative study of the construal of entities through nominal groups in Lhasa Tibetan and Mandarin Chinese. It approaches the grammatical description of nominal groups from the ideational and textual perspectives, and gives priority to the perspective “from above”, taking as point of departure the discourse semantic systems of ideation and identification. From the perspective of ideation, the comparison focuses on the classification, description and quantification of entities. From the perspective of identification, the comparison focuses on the presentation or presumption of entities in discourse, and the determination and qualification of them. In terms of grammatical realisations, the nucleus function of a nominal group, Thing, enters into multivariate structures with a range of pre- and post-Thing functions. However, configuration and realisation of the functions are language-specific. This study makes explicit structural consequences of systemic choices in nominal group grammar, and attends to the problem of structural markers, drawing on the notion of “subjacency” structure proposed in Martin et al. (2021) and Martin and Doran (this issue).

Reduced-order observer based output feedback control for a Timoshenko beam

This paper proposes observer based controls for a MIMO Timoshenko beam system with disturbances and references from an exosystem, and by further limiting the references and disturbances, also gives reduced-order controls. At first, we propose state feedback controls to guarantee the output regulation problem of a nominal Timoshenko beam system, which is obtained by specially choosing known disturbances and references. This also makes the PDE observer easily designed based on tracking errors only. Then, exosystem observers and their reduced-order forms are proposed in case of different geometric multiplicities and limited conditions of disturbances, references and system uncertainties. This gives observer based robust controls and reduced-order observer based controls. Robust output regulation is proved for the Timoshenko beam under observer based controls. Simulation examples are provided for a Timoshenko beam system with different references and system uncertainties.

Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time (PDT) constraint. A double-clock-dependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system, and assign to each system a controller scheduled by a clock. A necessary and sufficient convex stability criterion is presented for the nominal system, and is further extended to the stabilization controller design with a nominal clock. In the presence of bounded peak disturbances, another stabilization controller with an error clock is developed for the error system, with the purpose of “minimizing” the reachable set of the error system by the ellipsoidal techniques. It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system, i.e., a union of a family of bounding ellipsoids, that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system. Two numerical examples are provided to verify the effectiveness of the developed results.

Ripple Voltage Suppression of Dual Active Bridge Converter in Electric Locomotive Using H∞ Loop Shaping Control Method

The next-generation electric locomotive drive system has the problem of double grid frequency ripple voltage in the DC side of a single-phase PWM rectifier. In this paper, the intermediate stage dual-active-bridge DC-DC converter is studied, and an H∞ loop shaping ripple voltage suppression control strategy is proposed to restrain the harmonic voltage and optimize the dynamic and robust performance of the closed-loop system. Firstly, the mathematical model of the DAB closed-loop control system with fluctuating input voltage is established. Then, based on the H∞ loop shaping control theory, the dynamic performance, the ability of ripple voltage suppression, and the robust performance of the system are analyzed in the frequency domain. According to the results, a reasonable compensator is selected to reconstruct the magnitude frequency characteristic curve of the nominal system. After reconstruction, the solution of the robust stability margin of the corrected object is transformed into the H∞ robust control problem under the coprime factor uncertainty. The suboptimal H∞ robust controller is solved to obtain the best robustness boundary of the constructed system. Finally, the H∞ loop shaping ripple voltage suppression controller is obtained by combining the H∞ controller with the compensator. The experimental environment is set up in MATLAB-Simulink software. Compared with the traditional voltage loop control method and the input voltage feedforward control method, the dynamic performance of the proposed control strategy is slightly improved, and while within the allowable robust boundaries of the system, it has better ripple voltage suppression performance. When the system magnitude frequency curve is outside the tolerant robust stability margin, the ripple voltage suppression performance fails, but the harmonic content of output voltage is still far less than the other two control methods. The experiment results also prove the correctness of the theoretical analysis and that the proposed control method is effective and proper.

Stabilization of Nonlinear Systems with External Disturbances Using the DE-Based Control Method

This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied to asymptotically estimate the corresponding disturbances, and the disturbance estimators are presented and used to exactly eliminate the corresponding disturbances. Then, the disturbance estimator (DE)-based controllers are proposed to stabilize such nonlinear systems. It should be pointed out the unbounded disturbances are exactly estimated by suitable filters, which has advantages over the existing results. Finally, two illustrative examples, which have certain symmetrical properties, are taken, and the related numerical simulations are carried out to verify the effectiveness and correctness of the proposed results.

Robust Cause-Effect Chains with Bounded Execution Time and System-Level Logical Execution Time

In automotive and industrial real-time software systems, the primary timing constraints relate to cause-effect chains. A cause-effect chain is a sequence of linked tasks and it typically implements the process of reading sensor data, computing algorithms, and driving actuators. The classic timing analysis computes the maximum end-to-end latency of a given cause-effect chain to verify that its end-to-end deadline can be satisfied in all cases. This information is useful but not sufficient in practice: Software is usually evolving and updates may always alter the maximum end-to-end latency. It would be desirable to judge the quality of a software design a priori by quantifying how robust the timing of a given cause-effect chain will be in the presence of software updates. In this article, we derive robustness margins which guarantee that if software extensions stay within certain bounds, then the end-to-end deadline of a cause-effect chain can still be satisfied. Robustness margins are also useful to know if the system model has uncertain parameters. A robust system design can tolerate bounded deviations from the nominal system model without violating timing constraints. The results are applicable to both the bounded execution time programming model and the (system-level) logical execution time programming model. In this article, we study both an industrial use case from the automotive industry and analyze synthetically generated experiments with our open-source tool TORO.

Observer‐based robust optimal control for helicopter with uncertainties and disturbances

AbstractUnknown model uncertainties and external disturbances widely exist in helicopter dynamics and bring adverse effects on control performance. Optimal control techniques have been extensively studied for helicopters, but these methods cannot effectively handle flight control problems since they are sensitive to uncertainties and disturbances. This paper proposes an observer‐based robust optimal control scheme that enables a helicopter to fly optimally and reduce the influence of unknown model uncertainties and external disturbances. A control Lyapunov function (CLF) is firstly constructed using the backstepping method, then Sontag's formula is utilized to design an inverse optimal controller to stabilize the nominal system. Furthermore, it is stressed that the radial basis function (RBF) neural network is introduced to establish an observer with adaptive laws, approximating and compensating for the unknown model uncertainties and external disturbances to enhance the robustness of the closed‐loop system. The uniform ultimate boundedness of the closed‐loop system is ensured using the presented control approach via Lyapunov stability analysis. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control strategy.

Tube‐based batch model predictive control for polystyrene polymerization reaction process

AbstractThis paper focuses on product quality control issue of polystyrene polymerization reaction process. A novel tube‐based batch model predictive control (BMPC) strategy based on a data‐driven model is presented, which is inspired by the tube‐based robust model predictive control (MPC) strategy. First, the dynamic behavior of the polystyrene polymerization reaction process is captured with high accuracy by establishing a just‐in‐time learning (JITL) model. Then, the built JITL model is regarded as the nominal system, and a BMPC is designed on the basis of JITL model to obtain the nominal trajectory, which is an integrated control system framework composed of iterative learning control (ILC) and MPC. Meanwhile, another auxiliary MPC (AMPC) is designed to minimize the deviation between the actual trajectory and the nominal trajectory, and the actual tracking errors are limited to the tube invariant set centered on the nominal errors to restrain the performance deterioration of the control system caused by the modeling errors. Finally, the effectiveness of the proposed tube‐based BMPC method is verified by simulating an industrial batch polystyrene polymerization reaction process. The results indicate that the presented control algorithm not only enhances the tracking performance of the system but also provides a more robust system stability than existing methods. This paper provides a new solution to improve the product quality of polystyrene polymerization reaction process.

A Tube Model Predictive Control Method for Autonomous Lateral Vehicle Control Based on Sliding Mode Control.

This paper aims to enhance the lateral path tracking control of autonomous vehicles (AV) in the presence of external disturbances. While AV technology has made significant strides, real-world driving scenarios often pose challenges such as slippery or uneven roads, which can adversely affect the lateral path tracking control and reduce driving safety and efficiency. Conventional control algorithms struggle to address this issue due to their inability to account for unmodeled uncertainties and external disturbances. To tackle this problem, this paper proposes a novel algorithm that combines robust sliding mode control (SMC) and tube model predictive control (MPC). The proposed algorithm leverages the strengths of both MPC and SMC. Specifically, MPC is used to derive the control law for the nominal system to track the desired trajectory. The error system is then employed to minimize the difference between the actual state and the nominal state. Finally, the sliding surface and reaching law of SMC are utilized to derive an auxiliary tube SMC control law, which helps the actual system keep up with the nominal system and achieve robustness. Experimental results demonstrate that the proposed method outperforms conventional tube MPC, linear quadratic regulator (LQR) algorithms, and MPC in terms of robustness and tracking accuracy, especially in the presence of unmodeled uncertainties and external disturbances.

An Improved Model Predictive Control-Based Trajectory Planning Method for Automated Driving Vehicles Under Uncertainty Environments

For automated driving vehicles, trajectory planning is responsible for obtaining feasible trajectories with velocity profiles according to driving environments. From the perspective of trajectory planning, multiple uncertainties of environments and tracking deviations are two significant factors affecting driving safety. The former disturbs the judgment of trajectory planning on the environments, and the latter reduces the tracking accuracy of planned trajectories. To solve these problems, an improved model predictive control (MPC) trajectory planning method is proposed in this paper. Firstly, a Kalman filter fusion method is carried out to predict obstacle trajectory and their uncertainty, which combines model-based and data-based prediction methods. Based on the prediction results, a tube-based MPC trajectory planning method is applied to plan a reference trajectory with a small tracking deviation. The tube-based MPC is composed of two parts. One is the MPC with tightened constraints that is used to plan a feasible trajectory according to a nominal vehicle system and driving environment. The other is a state feedback control that is proposed to adjust the above planned trajectory to reduce the tracking deviations. To our knowledge, this paper proposes Kalman filter fusion and tube-based MPC planning method for the first time to consider the uncertainties of trajectory prediction and tracking control meanwhile in the planning. The planning method is verified by simulations and experiments in multiple scenes. Results show that the method is suitable for both static and dynamic scenes. Compared with applying the basic prediction method, the lateral deviation of the proposed method from the ideal trajectory is decreased by 46.5%. Compared with the nominal MPC method, the lateral tracking deviations of the proposed method are decreased by 77.42%.

Decentralized Current Sensorless Speed Synchronization With Feedback-Loop Adaptation for Multiservo System Applications

This study presents a parameter-independent decentralized speed synchronizer for multiservo systems without a current feedback loop, considering the current dynamics. The observer (not requiring system parameter information) exponentially estimates the speed derivative as updating the speed error to be vanished with the closed-loop pole-zero cancellation nature. The resultant estimates render it possible to implement the proposed decentralized synchronizer a the real-time feedback-loop adaptation, using only the nominal system parameter information. Two sets of QUBE-servo2 and myRIO1900 processors constitute the decentralized experimental platform to verify the closed-loop effectiveness.

Resilience of linear systems to partial loss of control authority

After a loss of control authority over thrusters of the Nauka module, the International Space Station lost attitude control for 45 min with potentially disastrous consequences. Motivated by this scenario, we investigate the continued capability of control systems to perform their task despite partial loss of authority over their actuators. We say that a system is resilient to such a malfunction if for any undesirable inputs and any target state there exists an admissible control driving the state to the target. Building on controllability conditions and differential games theory, we establish a necessary and sufficient condition for the resilience of linear systems. As their task might be time-constrained, ensuring completion alone is not sufficient. We also want to estimate how much slower the malfunctioning system is compared to its nominal performance. Relying on Lyapunov theory we derive analytical bounds on the reach times of the nominal and malfunctioning systems in order to quantify their resilience. We illustrate our work on the ADMIRE fighter jet model and on a temperature control system.

Mayoral elections and partisan dynamics in Africa’s local governments

ABSTRACT Enforcing party loyalty is particularly difficult in settings where parties are not strongly differentiated by policy or ideological platforms, as is the case in many African countries. Instead, the system of party nominations serves an important role in maintaining loyalty and discipline. Yet, direct mayoral elections at the subnational level affect these dynamics by expanding the range of positions that politicians can occupy, thereby creating opportunities for them to forge greater visibility within their party or enabling them to defect and create an independent political identity. Drawing on the case of Zambia, which shifted in 2016 from indirect to direct mayoral elections for its district councils, this article discusses how the change in electoral rules contributed to more independent mayoral candidates and growing intra-party frictions, especially among mayors governing large urban areas. Additional case studies from Senegal, which shifted to direct elections in 2022, and Mozambique, which reverted to indirect elections in 2018, further underscore the external validity of the analysis while refining its scope conditions. The article emphasizes that while political decentralization is often viewed as a mechanism for enhancing downwards accountability to citizens, it can also exert considerable impacts on party loyalty.

Decoupling design and control of a spaceborne ultra–stable platform for vibration isolation and precise steering

This study concerns the problems of system coupling and large payload mass ratio and designs a spaceborne ultra–stable platform (SUSP) to isolate the payload from the satellite vibration and accomplish high–precision payload steering. First, the dynamic equilibrium of the SUSP and vibration transfer functions are determined. The decoupling condition is then derived to make the coupled vibration transfer functions equal to zero, and the SUSP multi–input multi–output (MIMO) system is decoupled into six single–input single–output (SISO) subsystems. Consequently, the natural frequency matrix can be easily designed to guarantee the vibration isolation performance and obtain identical feedback gain values. Subsequently, a steering controller based on a nominal system simplified by decoupled dynamic equilibrium was designed. The impact of a large payload mass ratio was estimated and eliminated by the improved disturbance observer (IDO) in the steering controller. After rigid–flexible coupling dynamic modeling and analysis, two simulation stages were implemented. The results of the isolation stage exhibit a –40 dB/dec roll–off of the vibration disturbance and a coupled response reduction of approximately –20 dB. The payload tracking error of the isolation–steering integrated stage is reduced to 0.13″ (0.1° circular trace), and the isolation performance is further improved.

Robust model predictive tracking control for the wheeled mobile robot with boundary uncertain based on linear matrix inequalities

AbstractIn this study, a robust model predictive controller is designed for the trajectory tracking problem of non‐holonomic constrained wheeled mobile robot based on an elliptic invariant set approach. The controller is based on a time‐varying error model of robot kinematics and uses linear matrix inequalities to solve the robust tracking problem taking uncertainties into account. The uncertainties are modelled by linear fractional transform form to contain both parameter perturbations and external disturbances. The control strategy consists of a feedforward term that drives the centre of the ellipse to the reference point and a feedback term that converges the uncertain system state error to the equilibrium point. The strategy stabilises the nominal system and ensures that all states of the uncertain system remain within the ellipsoid at each step, thus achieving robust stability of the uncertain system. Finally, the robustness of the algorithm and its resistance to disturbances are verified by simulation and experiment.

H∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach

AbstractThis article investigates the ‐optimal estimation problem of a class of linear system with delays in states, disturbance input, and outputs. The estimator uses an extended Luenberger estimator format which estimates both the present and history states. The estimator is designed using an equivalent Partial Integral Equation (PIE) representation of the coupled nominal system. The advantage of the resulting PIE representation is compact and delay free—obviating the need for commonly used bounding technique such as integral inequalities which typically introduces conservatism into the resulting optimization problem. The ‐optimal estimator synthesis problem is then reformulated as a Linear Partial Inequality (LPI)—a form of convex optimization using operator variables and inequlities. Such LPI‐based optimization problems can be solved using semidefinite programming via the PIETOOLS toolbox in Matlab. Compared with previous work, the proposed method simplifies the analysis and computation process and resulting in observers which are non‐conservtism to 4 decimal places when compared with Pad‐based ODE observer design methodologies. Numerical examples and simulation results are given to illustrate the effectiveness and scalability of the proposed approach.

Transition-Dependent Bumpless Transfer Control Synthesis of Switched Linear Systems

This technical article is concerned with the bumpless transfer control synthesis of a class of discrete-time switched linear systems with general persistent dwell-time (PDT) switching signals. A novel piecewise transition-dependent controller facilitating the control synthesis is designed, which ensures the stability of the closed-loop system as well as the bumpless transfer at the occurrence of the switching. By imposing the given bumps limitation constraints, sufficient conditions on the existence of the controller are developed for the nominal systems. The results are extended to the case of the disturbed systems with an ensured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -gain. Numerical examples are provided to demonstrate the effectiveness and potential of the theoretical results.

Learning Reference Governor for Constrained Spacecraft Rendezvous and Proximity Maneuvering

Spacecraft automated rendezvous, proximity maneuvering, and docking (ARPOD) play significant roles in many space missions, including on-orbit servicing and active debris removal. Precise modeling and prediction of spacecraft dynamics can be challenging due to the uncertainties and perturbation forces in the spacecraft operating environment and due to the multilayered structure of its nominal control system. Despite this complication, spacecraft maneuvers need to satisfy required constraints (thrust limits, line-of-sight cone constraints, relative velocity of approach constraints, etc.) to ensure safety and achieve ARPOD objectives. This paper considers an application of a learning-based reference governor (LRG) to spacecraft ARPOD operations to enforce constraints without relying on a dynamic model of the spacecraft during the mission. Similar to the conventional reference governor (RG), the LRG is an add-on supervisor to a closed-loop control system, serving as a prefilter on the command generated by the ARPOD planner. The LRG modifies, if it becomes necessary, the reference command to a constraint-admissible value to enforce specified constraints. The LRG is distinguished, however, by the ability to rely on learning instead of an explicit model of the system; and it guarantees constraints’ satisfaction during and after the learning. In this paper, the LRG is applied to the control of combined translational and rotational motions of a chaser spacecraft, and three case studies with different sets of safety constraints and thruster assumptions are used to demonstrate the benefits of the LRG in ARPOD missions.

Event‐based robust performance guarantee for nonaffine plants via system identification

AbstractIn this paper, by making use of recurrent neural networks (RNNs), a novel event‐based robust optimal controller is designed for a category of continuous‐time (CT) nonlinear nonaffine systems with disturbances. For tackling the optimal‐robust problem transformation and the performance guarantee, a system identifier is developed to reconstruct the system, and an event‐triggered critic‐only strategy is investigated to replace the traditional time‐based actor‐critic structure. The RNN is adopted to reconstruct the nonaffine system as an identifier for obtaining the affine model. It simplifies the system structure and reduces computational burdens. In addition, the stability of the unknown nominal system learned by the RNN is proved. Then, using the obtained system identifier and the adaptive critic learning structure, the proposed event‐triggered robust control with performance guarantee is realized. At last, the effectiveness of the given design method is verified by two simulation examples.