Nonlinear model predictive missile control with a stabilising terminal constraint

Bachtiar, Vincent; Mühlpfordt, Tillmann; Moase, William H.; Faulwasser, Timm; Findeisen, Rolf; Manzie, Chris

doi:10.3182/20140824-6-za-1003.02122

Cited by 8 publications

(11 citation statements)

References 17 publications

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“…The first test case looks at a missile pitch-axis autopilot (PAA) adapted from [5]. The missile is flown at a cruising altitude and the autopilot is to control the missile to track a commanded acceleration.…”

Section: Test Plant Modelsmentioning

confidence: 99%

Analytical results for the multi-objective design of model-predictive control

Bachtiar

Manzie

Moase

et al. 2016

Control Engineering Practice

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In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -often with the latter as a fixed constraint -which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem.

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Section: Test Plant Modelsmentioning

confidence: 99%

Analytical results for the multi-objective design of model-predictive control

Bachtiar

Manzie

Moase

et al. 2016

Control Engineering Practice

View full text Add to dashboard Cite

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“…where the commanded fin deflection δ c rate is the input u of the system. Aerodynamic lift and moment are modeled to be cubic with respect to the angle of attack and linear with respect to the effective control surface deflection [11,18].…”

Section: Equations Of Motion a Missile Dynamicsmentioning

confidence: 99%

“…Parallel navigation relies on the fact that a zero LOS rate during engagement is a sufficient condition for the missile to intercept the target given that the missile is approaching the target (see, for example, [10]). Therefore, the control strategy employed will be to steer the missile such that the LOS rateλ, whose evolution is as described in (11), is regulated to zero.…”

Section: Control Formulation a Control Strategymentioning

confidence: 99%

Nonlinear Model-Predictive Integrated Missile Control and Its Multiobjective Tuning

Bachtiar

Manzie

Kerrigan

2017

Journal of Guidance, Control, and Dynamics

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I. Introduction Advanced missile control designs have been founded on recent developments aimed at a more streamlined engineering design approach to improve performance and cost of design. Central to these developments is the attempt for a full integration of subsystems to exploit any potential synergy. In missile control, much effort has been concentrated on integrating the autopilot and guidance subsystems [1, 2]. Such a unification of the control algorithm has direct benefits for the performance of the missile, primarily by removing the previously existing lag between the commanded and tracked acceleration from guidance and autopilot, respectively [3]. Several strategies have been proposed following this integrated control outlook, including sliding mode control [4, 5, 6], state feedback regulators [7, 8], as well as model-based approaches, for instance, a recently proposed linear quadratic regulation with model bias [9]. Model predictive control (MPC) is recognized for its ability in handling nonlinearities and constraints, therefore it is suited for high-performing agile missiles operated near constraints. This is demonstrated, for example, by the fact that the predominant proportional navigation (PN) in missile guidance is based on linear quadratic regulation [10], which is a special case of model-predictive control where constraints are absent and linear prediction model is used. Furthermore, the performance and feasibility of model-predictive missile autopilot has been studied in [11, 12]. Although promising a superior performance, MPC is typically associated with high levels of computational cost. Therefore, prior to the real-time realization of MPC, it is important to know the required computational capacity to implement MPC, especially in applications involving fast sampling rates such as missile control. A comprehensive offline tuning of MPC that balances both performance and cost is therefore needed before the implementation. In light of this, as a natural tuning method for an integrated autopilot and guidance algorithm, a multi-objective design approach that considers both closed-loop performance and required computational capacity allows for the comprehensive consideration of both algorithm and implementation designs of the system. A coupled approach in control tuning is known to be valuable due to its potential in streamlining the design process and produce system-optimal designs [13]. This allows for a more comprehensive analysis, such as the optimization of multiple underlying tuning/design objectives along with constraints, as introduced and discussed in [14]. This notion

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“…The control architecture considered in this paper is an MPC scheme with linear constraints and prediction model. For future work, typical extensions could include a nonlinear terminal constraint or nonlinear prediction model for the purpose of guaranteeing stability and better control performance [2]. With these extensions, the problem might involve more complex KKT conditions.…”

Section: Proof For a Perturbation Hmentioning

confidence: 99%

“…An OCP (2) with N prediction steps and h r = 0 has the same solution z * as that with N − 1 steps and h r = h, relying on the uniqueness of z * ( §3.4). z * has effectively the same dimension N for both cases.…”

Section: Lemma 7 (Continuity Of Zmentioning

confidence: 99%

Continuity and monotonicity of the MPC value function with respect to sampling time and prediction horizon

et al. 2016

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The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; sampling time and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used for developing optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity. This paper presents analytical results to reveal the smoothness properties of the MPC value function in open-and closed-loop for constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction steps are proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numerical investigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloop performance, particularly at faster sampling rates.

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Nonlinear model predictive missile control with a stabilising terminal constraint

Cited by 8 publications

References 17 publications

Analytical results for the multi-objective design of model-predictive control

Analytical results for the multi-objective design of model-predictive control

Nonlinear Model-Predictive Integrated Missile Control and Its Multiobjective Tuning

Continuity and monotonicity of the MPC value function with respect to sampling time and prediction horizon

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