Prescribed performance slide mode guidance law with terminal line-of-sight angle constraint against maneuvering targets

Abstract

This paper proposes a new terminal homing guidance law with line-of-sight angle constraint for a missile to intercept a noncooperative maneuvering target by integrating prescribed performance control with sliding mode control. The newly proposed guidance law is derived analytically with a prescribed performance controller in combination with the continuous nonsingular terminal sliding mode manifold and the disturbance observer. The prescribed performance controller is designed with a new prescribed performance function to avoid undesired abrupt change in the derivative of prescribed performance variable. In addition to its robustness and preciseness, this new homing guidance law is able to attenuate a largely abrupt change in guidance commands due to driving the sliding mode variable whose initial derivative is close to zero to a desired residual set at the beginning of the terminal homing phase. Furthermore, the time-varying control gain of the new guidance law is analytically determined by terminal tolerance. Theoretical analysis and numerical simulations are conducted to demonstrate the effectiveness of this new guidance law.

Appendix

The parameter $\alpha$ at $t\ge t_0$ is determined by following steps.

• Step 1 Determine an inequality

  $$\begin{aligned} \exp \left( {-\alpha \left( {t-t_0} \right) } \right) -1{+}\alpha \left( {t-t_0} \right) >\alpha \left( {t-t_0} \right) {-}1\nonumber \\ \end{aligned}$$

  (43)

• Step 2 Determine the interception initial time-to-go for missile as,

  $$\begin{aligned} t_{go} =\frac{R_f -R_0}{{\dot{R}}_0} \end{aligned}$$

  (44)

• Step 3 Determine the precision of PPV $\rho _1 (t_f, R_f)$ at terminal time

  

  (45)

  where $\zeta$ is a positive constant which satisfies $\zeta \le \rho _\mathrm{end}$ and $t_f$ represents the terminal time.

• Step 4 Determine the value of $\alpha$.

  $$\begin{aligned} \alpha\approx & {} \frac{\ln \left( {{\left( {\left. {s_e} \right| _{t=t_0} -\rho _\infty } \right) }/{\rho _1 \left( {t_f ,R_f } \right) }} \right) R_f}{R_0 t_{go}} \nonumber \\&+\,\frac{1+\Delta }{t_{go}} \end{aligned}$$

  (46)

  where $\Delta$ is a positive constant to speed up the convergence of $\rho _1 (t,R)$ and assure the terminal precision of $\rho _1 (t_f ,R_f)$.