Generalized formulation of linear nonquadratic weighted optimal error shaping guidance laws

This study presents a novel extension to the theory of optimal guidance laws represented by the nontraditional class of performance indices: nonquadratic-type signal Lp" role="presentation">Lp norm for the input weighted by an arbitrary positive function. Various missile guidance problems are generally formulated into a scalar terminal control problem based on the understanding of the predictor–corrector nature. Then, a new approach to derive the optimal feedback law, minimizing the nonquadratic performance index, is proposed by using the Hölderian inequality. The proposed extension allows a more general family of formulations for the design of closed-form feedback solutions to various guidance problems to be treated in a unified framework. The equivalence between the proposed approach and other design methodologies is investigated. In general, the type of input norm mainly determines the variability of input during the engagement while trading off against the rate of error convergence. The analytic solution derived in this study is verified by comparison with the solution from numerical optimization, and the effect of the exponent p" role="presentation">p in the performance index on the trajectory and command is demonstrated by numerical simulations

Optimal impact angle guidance for exo-atmospheric interception utilizing gravitational effect

This paper aims to develop a new optimal intercept angle guidance law for exo-atmospheric interception by utilizing gravity. A finite-time optimal regulation problem is formulated by considering the instantaneous zero-effort-miss (ZEM) and the intercept angle error as the system states. The analytical guidance command is then derived based on Schwarz's inequality approach and Lagrange multiplier concept. Capturability analysis using instantaneous linear time-invariant system concept is also presented to provide better insights of the proposed guidance law. Theoretical analysis reveals that the proposed optimal guidance law encompasses previously suggested optimal impact angle constrained guidance laws. Numerical simulations with some comparisons clearly demonstrate the effectiveness of the proposed guidance law

Integral global sliding mode guidance for impact angle control

This Correspondence proposes a new guidance law based on integral sliding mode control (ISMC) technique for maneuvering target interception with impact angle constraint. A time-varying function weighted line-of-sight (LOS) error dynamics, representing the nominal guidance performance, is introduced first. The proposed guidance law is derived by utilizing ISMC to follow the desired error dynamics. The convergence of the guidance law developed is supported by Lyapunov stability. Simulations with extensive comparisons explicitly demonstrate the effectiveness of the proposed approach

Optimal proportional-integral guidance with reduced sensitivity to target maneuvers

This paper proposes a new optimal guidance law based on proportional-integral (PI) concept to reduce the sensitivity to unknown target maneuvers. Compared to existing PI guidance laws, the proposed guidance command is derived in the optimal control framework while guaranteeing finite time convergence. The kinematics equation with respect to the zero-effortmiss (ZEM) is utilized and the integral ZEM is augmented as a new system state. The proposed guidance law is derived through the Schwarz's inequality method. The closed-form solution of proposed guidance law is presented to provide better insight of its properties. Additionally, the working principle of the integral command is investigated to show why the proposed guidance law is robust against unknown target accelerations. The analytical results reveal that the proposed optimal guidance law is exactly the same as an instantaneous direct model reference adaptive guidance law with a pre-specified reference model. The potential significance of the obtained results is that it can provide a point of connection between PI guidance laws and adaptive guidance laws. Therefore, it allows us to have better understanding of the physical meaning of both guidance laws and provides the possibility in designing a new guidance law that takes advantages of both approaches. Finally, the performance of the guidance law developed is demonstrated by nonlinear numerical simulations with extensive comparisons

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASAs Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach

Gravity-turn-assisted optimal guidance law

This paper proposes a new optimal guidance law that directly uses (instead of compensating for) gravity for accelerating missiles. The desired collision triangle that considers both gravity and the vehicle’s axial acceleration is analytically derived based on geometric conditions. The concept of instantaneous zero-effort-miss is introduced to allow for analytical guidance command derivation. By formulating a finite time instantaneous zero-effort-miss regulation problem, the proposed optimal guidance law is derived through Schwarz’s inequality approach. The relationships of the proposed formulation with conventional proportional navigation guidance and guidance-to-collision are analyzed, and the results show that the proposed guidance law encompasses previously suggested approaches. The significant contribution of the proposed guidance law lies in that it ensures zero final guidance command and enables energy saving with the aid of using gravity turn. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed approach

Impact angle control guidance synthesis for evasive maneuver against intercept missile

This paper proposes a synthesis of new guidance law to generate an evasive maneuver against enemy’s missile interception while considering its impact angle, acceleration, and field-of-view constraints. The first component of the synthesis is a new function of repulsive Artificial Potential Field to generate the evasive maneuver as a real-time dynamic obstacle avoidance. The terminal impact angle and terminal acceleration constraints compliance are based on Time-to-Go Polynomial Guidance as the second component. The last component is the Logarithmic Barrier Function to satisfy the field-of-view limitation constraint by compensating the excessive total acceleration command. These three components are synthesized into a new guidance law, which involves three design parameter gains. Parameter study and numerical simulations are delivered to demonstrate the performance of the proposed repulsive function and guidance law. Finally, the guidance law simulations effectively achieve the zero terminal miss distance, while satisfying an evasive maneuver against intercept missile, considering impact angle, acceleration, and field-of-view limitation constraints simultaneously

Unified control parametrisation approach for finite-horizon feedback control with trajectory shaping

This study presents control parametrisation as a unifying framework for designing a linear feedback control law that achieves finite-time transfer of output as well as trajectory shaping. Representing control input as a linear combination of independent basis functions allows wide variability in the resultant feedback control laws through selection of the number and types of basis functions. Given an array of basis functions that meets the trajectory shaping necessities, the unified design approach proceeds with determination of the coefficients so that the predicted trajectory attains the desired output at the final time. The input evaluated with the coefficients found at each instance essentially turns out to be a linear state feedback policy with an additional feedforward term and time-dependent gains which is appropriate for practical use. The unified control parametrisation approach lends itself well to missile guidance applications with the expandability and direct trajectory shaping capability that it provides. To emphasise expandability of the framework, this study revisits the trajectory shaping guidance laws from the control parametrisation viewpoint and shows how the notion of specifying input basis functions not only generalises various existing methods but also enables further extensions. Furthermore, an application to integrated guidance and control illustrates the strength of design process in handling the shaping requirements more directly through construction of appropriate basis