Search Results (20)

This paper presents the dynamic behavior of a nonlinear bioreactor model designed for fermentation processes, subject to temperature variations throughout the day. Ethanol production is presented by analyzing the fermenter’s temperature, which is controlled by the flow of the cooling fluid (water) that passes through the fermenter jacket. To optimize ethanol production during a period, a control design considering the optimal linear feedback control (OLFC) designed for nonlinear systems is introduced to control the flow of the cooling fluid of the bioreactor. Numerical and computational simulations demonstrated that the proposed control is efficient in maintaining the temperature at the desired levels and is resistant to parametric variations. With the results obtained from the optimal control (OLFC) and state-dependent Riccati equation (SDRE) control, a neuro-fuzzy control system is obtained, thus enabling the application of the proposed control in other bioreactor systems with similar dynamics. Full article

This paper presents the results of investigating the application of magnetorheological fluids in controlling the lateral and angular vibrations of a high-speed elevator. Numerical simulations are performed for a mathematical model with two degrees of freedom. The lateral and rotational accelerations are analyzed for different travel speeds to determine passenger comfort levels. To attenuate the elevator vibrations, the introduction of a magnetorheological damper in parallel with the passive damper of the elevator rollers is considered. To semi-actively control the dissipative forces of the magnetorheological fluids, a State-Dependent Riccati Equation (SDRE control) is proposed. The numerical results demonstrate that using an MR damper makes it possible to reduce the acceleration levels of the elevator cabin, thus improving passenger comfort and reducing the elevator’s vibration levels and wear on the mechanical and electronic components of the elevator. In addition to the results, a detailed sensitivity analysis is presented. Full article

Quad-tilt-wing (QTW) Unpiloted Aerial Vehicles (UAVs) combine the vertical takeoff and landing capabilities of rotary-wing designs with the high-speed, long-range performance of fixed-wing aircraft, offering significant advantages in both civil and military applications. The unique configuration of QTW UAVs presents complex control challenges due to nonlinear dynamics, strong coupling between translational and rotational motions, and significant variations in aerodynamic characteristics during transitions between flight modes. To address these challenges, this study develops an optimal control framework tailored for real-time operations. A State-Dependent Riccati Equation (SDRE) approach is employed for attitude control, addressing nonlinearities, while a Linear Quadratic Regulator (LQR) is used for position and velocity control to achieve robustness and optimal performance. By integrating these strategies and utilizing the inverse dynamics approach, the proposed control system ensures stable and efficient operation. This work provides a solution to the optimal control complexities of QTW UAVs, advancing their applicability in demanding and dynamic operational environments. Full article

This paper introduces a nonlinear Lyapunov-based Finite-Time State-Dependent Differential Riccati Equation (FT-SDDRE) control scheme, considering actuator saturation constraints and ensuring that the control system operates within safe operational limits designed for satellite reconfiguration and formation-keeping in low Earth orbit (LEO) missions. This control approach addresses the challenges of reaching the relative position and velocity vectors within a defined timeframe amid various orbital perturbations. The proposed approach guarantees precise formation control by utilizing a high-fidelity relative motion model that incorporates all zonal harmonics and atmospheric drag, which are the primary environmental disturbances in LEO. Additionally, the article presents an optimization methodology to determine the most efficient State-Dependent Coefficient (SDC) form regarding fuel consumption. This optimization process minimizes energy usage through a hybrid genetic algorithm and simulated annealing (HGASA), resulting in improved performance. In addition, this paper includes a sensitivity analysis to identify the optimized SDC parameterization for different satellite reconfiguration maneuvers. These maneuvers encompass radial, along-track, and cross-track adjustments, each with varying baseline distances. The analysis provides insights into how different parameterizations affect reconfiguration performance, ensuring precise and efficient control for each type of maneuver. The finite-time controller proposed here is benchmarked against other forms of SDRE controllers, showing reduced error margins. To further assess the control system’s effectiveness, an input saturation constraint is integrated, ensuring that the control system operates within safe operational limits, ultimately leading to the successful execution of the mission. Full article

In this work, we analyze the suitability of the State-Dependent Riccati Equation (SDRE) suboptimal nonlinear control formulation for the implementation of body-fixed hovering of a spacecraft in the highly nonlinear environment engendered by the faint force fields around single- and multi-body Near-Earth Objects (NEOs), a class of Small Solar System Bodies with high relevance either in scientific, economic, or planetary defense-related aspects. Our results, addressing the hovering of a spacecraft around relative equilibrium points on the effective potential of the Near-Earth Asteroid (16) Psyche and of the much smaller main body (called Alpha) of the triple NEA system (153591) 2001SN263, show that the known effectiveness offered by the flexibility engendered by state-dependent factorization of nonlinear models is also effective when applied in these faint and highly nonlinear force fields. In fact, this work is a qualitative evaluation of the suitability of using SDRE in the highly disturbed environment around Small Solar System Bodies, which has never been undertaken before. We intend to prove that this method is adequate. For real missions, it is necessary to make deeper studies. In particular, our results show the flexibility granted by the SDRE approach in the trade off between maneuvering time against fuel consumption, a central aspect in such space missions. For instance, our simulations showed control effort and time of convergence for two controlled trajectories around (16) Psyche ranging from a half-time convergence with ∼20 times lower cost. Analogously, for the much smaller bodies in the (153591) 2001SN263 triple system, we got two trajectories in which one of them may converge ∼10 times faster but with up to ∼100 times higher cost. Full article

Background/Objectives: Cancer is a dynamic and complex disease that remains largely untreated despite major advances in oncology and treatment. In this context, we aimed here to investigate optimal control techniques in the management of tumor growth inhibition, with a particular focus on cancer chemotherapy treatment strategies. Methods: Using both linear autoregressive with exogenous inputs (ARX) and advanced non-linear tumor growth inhibition (TGI) modeling approaches, we investigated various single-agent treatment protocols, including continuous, periodic, and intermittent chemotherapy schedules. By integrating advanced mathematical modeling with optimal control theory and methods, namely the Linear Quadratic Regulator (LQR) and the “pseudo-linear” state-space equivalent representation and suboptimal control of a non-linear dynamic system known as the State-Dependent Riccati Equation (SDRE) approach, this work explores and evaluates successfully, more effective chemotherapy treatment strategies at the computer simulation level, using real preclinical data which increases the expectation to be applied in the clinical practice of oncology. Results: The integration of these methods provides insights into how different drug administration schedules may affect tumor response at the preclinical level. This work uses mathematical modeling to evaluate the efficacy of various periodic and intermittent chemotherapy treatment strategies, with a focus on optimizing drug doses while minimizing the potential side effects of chemotherapy due to the administration of less effective chemotherapeutic doses. Conclusions: The treatment scenarios tested in this study could effectively stop tumor growth or even lead to tumor regression to a negligible or near-zero size. This approach highlights the importance of computational tools for more effective treatment strategies in chemotherapy and offers a promising direction for future research and more efficient clinical applications in oncology as part of a more individualized approach. Full article

The drag-free satellite plays an important role in the space-based gravitational wave observatory. The capture control of test mass after release is a crucial technology that can affect the success of the mission. The test mass must be released to the center of the electrostatic suspension cage accurately. This paper presents a nonlinear dynamic model of drag-free satellites in Lagrange formalism. A capture control scheme for test mass release phase is proposed based on the state-dependent Riccati equation (SDRE) strategy. To deal with the actuator saturation problem, a nonlinear saturation model is introduced to the dynamics of satellite, while the SDRE strategy is applied to the non-affine system. The effectiveness of the proposed methodology is verified by the numerical simulation for the drag-free satellite. Full article

Permanent Magnet Synchronous Motors (PMSMs) with high energy efficiency, reliable performance, and a relatively simple structure are widely utilised in various applications. In this paper, a suboptimal controller is proposed for PMSMs without sensors based on the state-dependent Riccati equation (SDRE) technique combined with customised impulsive observers (IOs). Here, the SDRE technique facilitates a pseudo-linearised display of the motor with state-dependent coefficients (SDCs) while preserving all its nonlinear features. Considering the risk of non-available/non-measurable states in the motor due to sensor and instrumentation costs, the SDRE is combined with IOs to estimate the PMSM speed and position states. Customised IOs are proven to be capable of obtaining quality, continuous estimates of the motor states despite the discrete format of the output signals. The simulation results in this work illustrate an accurate state estimation and control mechanism for the speed of the PMSM in the presence of load torque disturbances and reference speed changes. It is clearly shown that the SDRE-IO design is superior compared to the most popular existing regulators in the literature for sensorless speed control. Full article

The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution. Full article

This paper presents the results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior. Numerical results using phase portraits, bifurcation diagrams, Lyapunov exponents, and 0-1 testing confirmed chaotic and hyperchaotic behavior. The results also proved the effectiveness of the control, showing errors below 1%, even in cases where the control design is subject to parametric errors. Additionally, an investigation of the system in fractional order is included, demonstrating that the system has periodic, constant, or chaotic behavior for specific values of the order of the derivative. Full article

Deep space missions, and particularly cislunar endeavors, are becoming a major field of interest for the space industry, including for the astrodynamics research community. While near-Earth missions may be completely covered by perturbed Keplerian dynamics, deep space missions require a different modeling approach, where multi-body gravitational interactions play a major role. To this end, the Restricted Three-Body Problem stands out as an insightful first modeling strategy for early mission design purposes, retaining major dynamical transport structures while still being relatively simple. Dynamical Systems Theory and classical Hamiltonian Mechanics have proven themselves as remarkable tools to analyze deep-space missions within this context, with applications ranging from ballistic capture trajectory design to stationkeeping. In this work, based on this premise, a Hamiltonian derivation of the Restricted Three-Body Problem co-orbital dynamics between two spacecraft is introduced in detail. Thanks to the analytical and numerical models derived, connections between the relative and classical Keplerian and CR3BP problems are shown to exist, including first-order linear solutions and an inherited Hamiltonian normal form. The analytical linear and higher-order models derived allow the theoretical finding and unveiling of natural co-orbital phase space structures, including relative periodic and quasi-periodic orbital families, which are further exploited for general proximity operation applications. In particular, a novel reduced-order, optimal low-thrust stationkeeping controller is derived in the relative Floquet phase space, hybridizing the classical State Dependent Ricatti Equation (SDRE) with Koopman control techniques for efficient unstable manifold regulation. The proposed algorithm is demonstrated and validated within several end-to-end low-cost stationkeeping missions, and comparison against classical continuous stationkeeping algorithms presented in the literature is also addressed to reveal its enhanced performance. Finally, conclusions and open lines of research are discussed. Full article

In this paper, a planar air-bearing test bed with unmanned aerial vehicles (UAV) was used to test a microsatellite motion control system. The UAV mock-ups were controlled by four ventilator actuators that imitated the satellite thrusters and provided the required acceleration vector in the horizontal plane, and torque along the vertical direction. The mock-ups moved almost without friction along the planar air-bearing test bed due to the air cushion between the test bed surface and the flat mock-up base. The motion of the mock-ups motion imitated the motion of satellites in the orbital plane. The problem of space debris can be solved using special microsatellite missions able to dock to space debris objects and change their orbit. In this paper, two control algorithms based on the virtual potentials approach and the State Dependent Ricatti Equation (SDRE) controller, were proposed for docking to a non-cooperative space debris object. The algorithms were tested in a laboratory facility, and the results are presented and analyzed, including their main features demonstrated during the laboratory study. It was shown that the SDRE-based control was faster, although the virtual potential-based control required less characteristic velocity. Full article

In the paper, a new cascade control system for an autonomous flight of an unmanned aerial vehicle (UAV) based on Proportional–Integral–Derivative (PID) and finite-time State-Dependent Riccati Equation (SDRE) control is proposed. The PID and SDRE controllers are used in a hybrid control system for precise control and stabilization, which is necessary to increase the drone’s flight stability and maneuver precision. The hybrid PID-SDRE control system proposed for the quadrotor model is quasi-optimal, since the suboptimal control algorithm for the UAV stabilization is used. The combination of the advantages of PID and SDRE control gives a significant improvement in the quality of control while maintaining the simplicity of the control system. Furthermore, the use of the suboptimal control technique provides the UAV attitude tracking in finite time. These remarks are drawn from a series of simulation tests conducted for the drone model. Full article

For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation (PA) of the solution of the initial problem for the discrete matrix Riccati equation is constructed based on the state-dependent Riccati equation (SDRE) approach and the asymptotics by the small-step of the boundary layer functions method. The symmetric gain coefficients matrix for Padé control synthesis is constructed based on the one-point PA. As a result, the parametric closed-loop control is obtained. The results of numerical experiments illustrate, in particular, the improved extrapolation properties of the constructed regulator, which makes the algorithm applicable in control systems for a wider range of parameter variation. Full article

This paper presents modeling and infinite-time suboptimal control of a quadcopter device using the state-dependent Riccati equation (SDRE) method. It establishes a solution to the control problem using SDRE and proposes a new procedure for solving the problem. As a new contribution, the paper proposes a modified SDRE-based suboptimal control technique for affine nonlinear systems. The method uses a pseudolinearization of the closed-loop system employing Moore–Penrose pseudoinverse. Then, the algebraic Riccati equation (ARE), related to the feedback compensator gain, is reduced to state-independent form, and the solution can be computed only once in the whole control process. The ARE equation is applied to the problem reported in this study that provides general formulation and stability analysis. The effectiveness of the proposed control technique is demonstrated through the use of simulation results for a quadrotor device. Full article